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doc/talks/2024-02-03-fosdem/.gitignore
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doc/talks/2024-02-03-fosdem/abstract.md
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### (fr) Garage, un système de stockage de données géo-distribué léger et robuste
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Garage est un système de stockage de données léger, géo-distribué, qui
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implémente le protocole de stockage S3 de Amazon. Garage est destiné
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principalement à l'auto-hébergement sur du matériel courant d'occasion. À ce
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titre, il doit tolérer un grand nombre de pannes: coupures de courant, coupures
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de connexion Internet, pannes de machines, ... Il doit également être facile à
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déployer et à maintenir, afin de pouvoir être facilement utilisé par des
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amateurs ou des petites organisations.
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Cette présentation vous proposera un aperçu de Garage et du choix technique
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principal qui rend un système comme Garage possible: le refus d'utiliser des
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algorithmes de consensus, remplacés avantageusement par des méthodes à
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cohérence faible. Notre modèle est fortement inspiré de la base de donnée
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Dynamo (DeCandia et al, 2007), et fait usage des types de données CRDT (Shapiro
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et al, 2011). Nous exploreront comment ces méthodes s'appliquent à la
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construction de l'abstraction "stockage objet" dans un système distribué, et
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quelles autres abstractions peuvent ou ne peuvent pas être construites dans ce
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modèle.
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### (en) Garage, a lightweight and robust geo-distributed data storage system
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Garage is a lightweight geo-distributed data store that implements the Amazon
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S3 object storage protocol. Garage is meant primarily for self-hosting at home
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on second-hand commodity hardware, meaning it has to tolerate a wide variety of
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failure scenarios such as power cuts, Internet disconnections and machine
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crashes. It also has to be easy to deploy and maintain, so that hobbyists and
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small organizations can use it without trouble.
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This talk will present Garage and the key technical choice that made Garage
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possible: refusing to use consensus algorithms and using instead weak
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consistency methods, with a model that is loosely based on that of the Dynamo
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database (DeCandia et al, 2007) and that makes heavy use of conflict-free
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replicated data types (Shapiro et al, 2011). We will explore how these methods
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are suited to building the "object store" abstraction in a distributed system,
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and what other abstractions are possible or impossible to build in this model.
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After Width: | Height: | Size: 18 KiB |
536
doc/talks/2024-02-03-fosdem/assets/lattice5.svg
Normal file
536
doc/talks/2024-02-03-fosdem/assets/lattice5.svg
Normal file
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@ -0,0 +1,536 @@
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|
y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
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|
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xml:space="preserve"
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|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
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|
y="33.02087">$\sqsupseteq \{a\} \to$ OK</tspan></text>
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|
<text
|
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|
xml:space="preserve"
|
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|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
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|
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|
xml:space="preserve"
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|
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|
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|
y="52.022549">return OK</tspan></text>
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|
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|
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|
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|
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|
y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
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|
y="33.02087">$\sqsupseteq \{a\} \to$ OK</tspan></text>
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|
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|
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|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
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|
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style="fill:#000000;stroke-width:0.264583"
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|
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|
y="73.643356">$\to \{\}$</tspan></text>
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|
xml:space="preserve"
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|
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|
style="fill:#000000;stroke-width:0.264583"
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|
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|
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|
y="52.022549">return OK</tspan></text>
|
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|
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|
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|
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|
After Width: | Height: | Size: 19 KiB |
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581
doc/talks/2024-02-03-fosdem/assets/lattice7.svg
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|
cx="18.004833"
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cy="30.371933"
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|
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|
<circle
|
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|
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
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|
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|
cx="18.004833"
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|
cy="21.341394"
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|
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|
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|
y="13.702217"
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|
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|
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|
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|
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x="6.9525447"
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|
x="6.9525447"
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|
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|
id="text3707-1"><tspan
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|
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id="tspan3705-5"
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|
style="fill:#000000;stroke-width:0.264583"
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|
x="6.9525447"
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|
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|
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|
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|
xml:space="preserve"
|
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|
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|
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|
x="23.457415"
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|
y="24.042637"
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|
id="text3750"><tspan
|
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|
sodipodi:role="line"
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id="tspan3748"
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|
style="fill:#000000;stroke-width:0.264583"
|
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|
x="23.457415"
|
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|
y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
|
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|
<text
|
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|
xml:space="preserve"
|
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|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
|
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|
x="23.457415"
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id="text3750-3"><tspan
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|
style="fill:#000000;stroke-width:0.264583"
|
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|
x="23.457415"
|
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|
y="33.02087">$\sqsupseteq \{a\} \to$ OK</tspan></text>
|
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|
<text
|
||||||
|
xml:space="preserve"
|
||||||
|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
|
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|
x="23.457415"
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|
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id="text3750-0"><tspan
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|
sodipodi:role="line"
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id="tspan3748-6"
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|
style="fill:#000000;stroke-width:0.264583"
|
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|
x="23.457415"
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|
y="41.972523">$\sqsupseteq \{a\}$</tspan></text>
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|
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|
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|
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|
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|
cx="18.004833"
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|
cy="70.942116"
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|
r="2.7302806" />
|
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|
<text
|
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|
xml:space="preserve"
|
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|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
|
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|
x="23.457415"
|
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|
y="73.643356"
|
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|
id="text3750-7"><tspan
|
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|
sodipodi:role="line"
|
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|
id="tspan3748-65"
|
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|
style="fill:#000000;stroke-width:0.264583"
|
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|
x="23.457415"
|
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|
y="73.643356">$\to \{\}$</tspan></text>
|
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|
<text
|
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|
xml:space="preserve"
|
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|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
|
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|
x="14.395845"
|
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|
y="52.022549"
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|
id="text4280"><tspan
|
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|
sodipodi:role="line"
|
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|
id="tspan4278"
|
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|
style="fill:#000000;stroke-width:0.264583"
|
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|
x="14.395845"
|
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|
y="52.022549">return OK</tspan></text>
|
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|
<text
|
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|
xml:space="preserve"
|
||||||
|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
|
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|
x="14.395845"
|
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|
y="92.005798"
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|
id="text4280-3"><tspan
|
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|
sodipodi:role="line"
|
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|
id="tspan4278-7"
|
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|
style="fill:#000000;stroke-width:0.264583"
|
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|
x="14.395845"
|
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|
y="92.005798">return $\{\}\sqcup\{a\}=\{a\}$</tspan></text>
|
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|
<circle
|
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|
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
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|
id="path3663-1-5"
|
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|
cx="18.004833"
|
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|
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|
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|
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|
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|
<text
|
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|
xml:space="preserve"
|
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|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
|
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|
x="23.457415"
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|
y="83.577797"
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|
id="text3750-0-6"><tspan
|
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|
sodipodi:role="line"
|
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|
id="tspan3748-6-9"
|
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|
style="fill:#000000;stroke-width:0.264583"
|
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|
x="23.457415"
|
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|
y="83.577797">$\to \{a\}$</tspan></text>
|
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|
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|
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|
</svg>
|
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|
After Width: | Height: | Size: 20 KiB |
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doc/talks/2024-02-03-fosdem/assets/latticeB_1.svg
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576
doc/talks/2024-02-03-fosdem/assets/latticeB_1.svg
Normal file
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|
height="600"
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|
viewBox="0 0 264.58333 158.75"
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|
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y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
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xml:space="preserve"
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style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
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style="fill:#999999;stroke-width:0.264583"
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x="23.457415"
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y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
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xml:space="preserve"
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style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
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x="23.457415"
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style="fill:#999999;stroke-width:0.264583"
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x="23.457415"
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y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
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cx="18.004833"
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style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
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cx="18.004833"
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r="2.7302806" />
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cx="18.004833"
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x="6.9525447"
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style="fill:#000000;stroke-width:0.264583"
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x="6.9525447"
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|
y="65.279381">$write(\{b\})$:</tspan></text>
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<text
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xml:space="preserve"
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style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
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x="59.340172"
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id="text3707-5-3"><tspan
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|
x="23.457415"
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|
y="75.619804"
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|
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|
style="fill:#999999;stroke-width:0.264583"
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|
x="23.457415"
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|
y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text>
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|
<text
|
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|
xml:space="preserve"
|
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|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
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x="23.457415"
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id="text3750-3-4"><tspan
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|
x="23.457415"
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|
y="84.598038">$\sqsupseteq \{b\} \to$ OK</tspan></text>
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|
<text
|
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|
xml:space="preserve"
|
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|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
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|
style="fill:#999999;stroke-width:0.264583"
|
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|
x="23.457415"
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|
y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
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|
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|
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|
cx="118.63729"
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|
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|
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|
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|
<circle
|
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|
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|
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|
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|
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|
<text
|
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|
xml:space="preserve"
|
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|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
|
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|
x="72.653946"
|
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|
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|
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|
id="text3750-9"><tspan
|
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|
sodipodi:role="line"
|
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|
id="tspan3748-3"
|
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|
style="fill:#000000;stroke-width:0.264583"
|
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|
x="72.653946"
|
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|
y="127.6125">$\to \{a\}$</tspan></text>
|
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|
<text
|
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|
xml:space="preserve"
|
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|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
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|
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|
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id="text4280-6"><tspan
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|
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|
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id="tspan2630">return $\{a\}$</tspan></text>
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|
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|
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|
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|
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|
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|
r="2.7302806" />
|
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|
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|
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|
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|
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|
x="72.653946"
|
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|
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|
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|
style="fill:#000000;stroke-width:0.264583"
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|
x="72.653946"
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|
y="136.59073">$\to \{\}$</tspan></text>
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
id="text3750-9-1"><tspan
|
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|
sodipodi:role="line"
|
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|
id="tspan3748-3-8"
|
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|
style="fill:#000000;stroke-width:0.264583"
|
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|
x="179.81555"
|
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|
y="127.6125">$\to \{\}$</tspan></text>
|
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|
<text
|
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|
xml:space="preserve"
|
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|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
|
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|
x="162.7999"
|
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|
y="118.94403"
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id="text3707-5-3-7"><tspan
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|
sodipodi:role="line"
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|
id="tspan3705-4-6-5"
|
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|
style="fill:#000000;stroke-width:0.264583"
|
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|
x="162.7999"
|
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|
y="118.94403">$read()$:</tspan></text>
|
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|
<text
|
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|
xml:space="preserve"
|
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|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583"
|
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|
x="134.97845"
|
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|
y="132.58472"
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id="text3899"><tspan
|
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sodipodi:role="line"
|
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id="tspan3897"
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style="stroke-width:0.264583"
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|
x="134.97845"
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|
y="132.58472">;</tspan></text>
|
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|
<text
|
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|
xml:space="preserve"
|
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|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
|
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|
x="169.92604"
|
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|
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id="text4280-6-7"><tspan
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|
sodipodi:role="line"
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|
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|
x="169.92604"
|
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|
y="146.3129"
|
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|
id="tspan2630-9">return $\{b\}$</tspan></text>
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|
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|
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|
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|
<text
|
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|
xml:space="preserve"
|
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|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
|
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|
x="179.81555"
|
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|
y="136.59073"
|
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|
id="text3750-3-6-0"><tspan
|
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|
sodipodi:role="line"
|
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|
id="tspan3748-2-0-2"
|
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|
style="fill:#000000;stroke-width:0.264583"
|
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|
x="179.81555"
|
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|
y="136.59073">$\to \{b\}$</tspan></text>
|
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|
<text
|
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|
xml:space="preserve"
|
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|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:end;text-anchor:end;fill:#ff0000;stroke-width:0.264583"
|
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|
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|
sodipodi:role="line"
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|
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|
style="fill:#ff0000;stroke-width:0.264583"
|
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|
x="259.75"
|
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|
y="135.53111">${\Large\textbf{??!}}$~~~~~</tspan><tspan
|
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|
sodipodi:role="line"
|
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|
style="fill:#ff0000;stroke-width:0.264583"
|
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|
x="259.75"
|
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|
y="146.11446"
|
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|
id="tspan9372">$\{a\} \not\sqsubseteq \{b\}$</tspan></text>
|
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|
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|
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doc/talks/2024-02-03-fosdem/assets/latticeB_2.svg
Normal file
576
doc/talks/2024-02-03-fosdem/assets/latticeB_2.svg
Normal file
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id="tspan1007-5"
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style="fill:#000000;stroke-width:0.264583"
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|
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|
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|
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|
id="g1183"
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|
<text
|
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xml:space="preserve"
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|
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x="112.90984"
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id="text1117"><tspan
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id="tspan1115"
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|
style="fill:#000000;stroke-width:0.264583"
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|
y="40.841526">$\{a,c\}$</tspan></text>
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||||||
|
<text
|
||||||
|
xml:space="preserve"
|
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|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
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|
x="49.27084"
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id="text1117-3"><tspan
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y="40.841526">$\{a,b\}$</tspan></text>
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|
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|
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xml:space="preserve"
|
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|
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|
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x="176.20593"
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id="text1117-6"><tspan
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|
x="176.20593"
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|
y="40.841526">$\{b,c\}$</tspan></text>
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|
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d="M 153.33622,90.367682 118.34198,73.428915"
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id="path1300" />
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|
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|
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|
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d="M 177.46016,90.367682 212.4544,73.428915"
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|
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sodipodi:nodetypes="cc" />
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|
<path
|
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|
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|
sodipodi:nodetypes="cc" />
|
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|
<path
|
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|
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
|
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|
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|
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sodipodi:nodetypes="cc" />
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|
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|
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|
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|
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|
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cy="95.24971"
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|
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|
<circle
|
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|
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|
cx="176.97627"
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cy="68.155472"
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|
r="2.7302806" />
|
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|
<circle
|
||||||
|
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
|
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|
id="path3663-1"
|
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|
cx="18.004833"
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|
cy="39.402473"
|
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|
r="2.7302806" />
|
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|
<circle
|
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|
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|
id="path3663-3-0"
|
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|
cx="18.004833"
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|
cy="30.371933"
|
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|
r="2.7302806" />
|
||||||
|
<circle
|
||||||
|
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
|
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|
id="path3663-6-6"
|
||||||
|
cx="18.004833"
|
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|
cy="21.341394"
|
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|
r="2.7302806" />
|
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|
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|
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|
xml:space="preserve"
|
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|
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|
||||||
|
x="6.9525447"
|
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|
y="13.702217"
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|
id="text3707"><tspan
|
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|
sodipodi:role="line"
|
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|
id="tspan3705"
|
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|
style="fill:#000000;stroke-width:0.264583"
|
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|
x="6.9525447"
|
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|
y="13.702217">$write(\{a\})$:</tspan></text>
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|
<text
|
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|
xml:space="preserve"
|
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|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
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|
y="24.042637"
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|
id="text3750"><tspan
|
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|
sodipodi:role="line"
|
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|
id="tspan3748"
|
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|
style="fill:#000000;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
||||||
|
y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
|
||||||
|
<text
|
||||||
|
xml:space="preserve"
|
||||||
|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
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|
y="33.02087"
|
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|
id="text3750-3"><tspan
|
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|
sodipodi:role="line"
|
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|
id="tspan3748-2"
|
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|
style="fill:#999999;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
||||||
|
y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
|
||||||
|
<text
|
||||||
|
xml:space="preserve"
|
||||||
|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
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|
y="41.972523"
|
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|
id="text3750-0"><tspan
|
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|
sodipodi:role="line"
|
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|
id="tspan3748-6"
|
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|
style="fill:#999999;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
||||||
|
y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
|
||||||
|
<circle
|
||||||
|
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
|
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|
id="path3663-1-4"
|
||||||
|
cx="18.004833"
|
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|
cy="90.979645"
|
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|
r="2.7302806" />
|
||||||
|
<circle
|
||||||
|
style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
|
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|
id="path3663-3-0-5"
|
||||||
|
cx="18.004833"
|
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|
cy="81.949104"
|
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|
r="2.7302806" />
|
||||||
|
<circle
|
||||||
|
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
|
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|
id="path3663-6-6-2"
|
||||||
|
cx="18.004833"
|
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|
cy="72.918564"
|
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|
r="2.7302806" />
|
||||||
|
<text
|
||||||
|
xml:space="preserve"
|
||||||
|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
|
||||||
|
x="6.9525447"
|
||||||
|
y="65.279381"
|
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|
id="text3707-5"><tspan
|
||||||
|
sodipodi:role="line"
|
||||||
|
id="tspan3705-4"
|
||||||
|
style="fill:#000000;stroke-width:0.264583"
|
||||||
|
x="6.9525447"
|
||||||
|
y="65.279381">$write(\{b\})$:</tspan></text>
|
||||||
|
<text
|
||||||
|
xml:space="preserve"
|
||||||
|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
|
||||||
|
x="59.340172"
|
||||||
|
y="118.94403"
|
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|
id="text3707-5-3"><tspan
|
||||||
|
sodipodi:role="line"
|
||||||
|
id="tspan3705-4-6"
|
||||||
|
style="fill:#000000;stroke-width:0.264583"
|
||||||
|
x="59.340172"
|
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|
y="118.94403">$read()$:</tspan></text>
|
||||||
|
<text
|
||||||
|
xml:space="preserve"
|
||||||
|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
||||||
|
y="75.619804"
|
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|
id="text3750-7"><tspan
|
||||||
|
sodipodi:role="line"
|
||||||
|
id="tspan3748-4"
|
||||||
|
style="fill:#999999;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
||||||
|
y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text>
|
||||||
|
<text
|
||||||
|
xml:space="preserve"
|
||||||
|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
||||||
|
y="84.598038"
|
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|
id="text3750-3-4"><tspan
|
||||||
|
sodipodi:role="line"
|
||||||
|
id="tspan3748-2-3"
|
||||||
|
style="fill:#000000;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
||||||
|
y="84.598038">$\sqsupseteq \{b\} \to$ OK</tspan></text>
|
||||||
|
<text
|
||||||
|
xml:space="preserve"
|
||||||
|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
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|
y="93.54969"
|
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|
id="text3750-0-0"><tspan
|
||||||
|
sodipodi:role="line"
|
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|
id="tspan3748-6-7"
|
||||||
|
style="fill:#999999;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
||||||
|
y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
|
||||||
|
<circle
|
||||||
|
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
|
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|
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|
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y="13.151893">$\{a,b,c\}$</tspan></text>
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|
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|
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|
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|
y="67.008698">$\{a\}$</tspan></text>
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|
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|
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|
xml:space="preserve"
|
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|
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|
x="112.90984"
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id="text1009-3"><tspan
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|
style="fill:#000000;stroke-width:0.264583"
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|
x="112.90984"
|
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|
y="67.017166">$\{b\}$</tspan></text>
|
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|
<text
|
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|
xml:space="preserve"
|
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|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
|
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|
x="176.20593"
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|
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id="text1009-7"><tspan
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|
sodipodi:role="line"
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|
id="tspan1007-5"
|
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|
style="fill:#000000;stroke-width:0.264583"
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|
x="176.20593"
|
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|
y="67.008698">$\{c\}$</tspan></text>
|
||||||
|
</g>
|
||||||
|
<g
|
||||||
|
id="g1183"
|
||||||
|
transform="translate(51.996784,1.0317046)"
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|
style="fill:#000000">
|
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|
<text
|
||||||
|
xml:space="preserve"
|
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|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
|
||||||
|
x="112.90984"
|
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|
y="40.841526"
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|
id="text1117"><tspan
|
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|
sodipodi:role="line"
|
||||||
|
id="tspan1115"
|
||||||
|
style="fill:#000000;stroke-width:0.264583"
|
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|
x="112.90984"
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||||||
|
y="40.841526">$\{a,c\}$</tspan></text>
|
||||||
|
<text
|
||||||
|
xml:space="preserve"
|
||||||
|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
|
||||||
|
x="49.27084"
|
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|
y="40.841526"
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|
id="text1117-3"><tspan
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|
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id="tspan1115-5"
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|
style="fill:#000000;stroke-width:0.264583"
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|
x="49.27084"
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|
y="40.841526">$\{a,b\}$</tspan></text>
|
||||||
|
<text
|
||||||
|
xml:space="preserve"
|
||||||
|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
|
||||||
|
x="176.20593"
|
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|
y="40.841526"
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|
id="text1117-6"><tspan
|
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|
sodipodi:role="line"
|
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id="tspan1115-2"
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|
style="fill:#000000;stroke-width:0.264583"
|
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|
x="176.20593"
|
||||||
|
y="40.841526">$\{b,c\}$</tspan></text>
|
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|
</g>
|
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|
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|
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|
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
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|
d="M 153.33622,90.367682 118.34198,73.428915"
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|
id="path1300" />
|
||||||
|
<path
|
||||||
|
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
|
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|
d="M 177.46016,90.367682 212.4544,73.428915"
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|
id="path1300-2" />
|
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|
<path
|
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|
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
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d="M 153.33622,61.655656 118.34198,44.716889"
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id="path1300-0" />
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|
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|
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|
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|
d="M 177.46016,61.655656 212.4544,44.716889"
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id="path1300-2-6" />
|
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|
<path
|
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|
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
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d="M 118.34198,61.655656 153.33622,44.716889"
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id="path1300-0-7" />
|
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|
<path
|
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style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
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d="M 118.34198,34.227412 153.33622,17.288645"
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id="path1300-0-7-5" />
|
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|
<path
|
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d="M 212.4544,34.227412 177.46016,17.288645"
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id="path1300-2-6-9-0" />
|
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|
<path
|
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|
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
|
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d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
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sodipodi:nodetypes="cc" />
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|
<path
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|
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id="path1300-2-2-9"
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|
sodipodi:nodetypes="cc" />
|
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|
<path
|
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|
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
|
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|
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|
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|
id="path1300-2-2-6"
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|
sodipodi:nodetypes="cc" />
|
||||||
|
<path
|
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|
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
|
||||||
|
d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
|
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|
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sodipodi:nodetypes="cc" />
|
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|
<circle
|
||||||
|
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|
id="path3663"
|
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|
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cy="95.24971"
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|
r="2.7302806" />
|
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|
<circle
|
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style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
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|
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|
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|
cx="176.97627"
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|
cy="68.155472"
|
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|
r="2.7302806" />
|
||||||
|
<circle
|
||||||
|
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
|
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|
id="path3663-1"
|
||||||
|
cx="18.004833"
|
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|
cy="39.402473"
|
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|
r="2.7302806" />
|
||||||
|
<circle
|
||||||
|
style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
|
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|
id="path3663-3-0"
|
||||||
|
cx="18.004833"
|
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|
cy="30.371933"
|
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|
r="2.7302806" />
|
||||||
|
<circle
|
||||||
|
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
|
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|
id="path3663-6-6"
|
||||||
|
cx="18.004833"
|
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|
cy="21.341394"
|
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|
r="2.7302806" />
|
||||||
|
<text
|
||||||
|
xml:space="preserve"
|
||||||
|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
|
||||||
|
x="6.9525447"
|
||||||
|
y="13.702217"
|
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|
id="text3707"><tspan
|
||||||
|
sodipodi:role="line"
|
||||||
|
id="tspan3705"
|
||||||
|
style="fill:#000000;stroke-width:0.264583"
|
||||||
|
x="6.9525447"
|
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|
y="13.702217">$write(\{a\})$:</tspan></text>
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|
<text
|
||||||
|
xml:space="preserve"
|
||||||
|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
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|
y="24.042637"
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|
id="text3750"><tspan
|
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|
sodipodi:role="line"
|
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|
id="tspan3748"
|
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|
style="fill:#000000;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
||||||
|
y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
|
||||||
|
<text
|
||||||
|
xml:space="preserve"
|
||||||
|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
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|
y="33.02087"
|
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|
id="text3750-3"><tspan
|
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|
sodipodi:role="line"
|
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|
id="tspan3748-2"
|
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|
style="fill:#999999;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
||||||
|
y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
|
||||||
|
<text
|
||||||
|
xml:space="preserve"
|
||||||
|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
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|
y="41.972523"
|
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|
id="text3750-0"><tspan
|
||||||
|
sodipodi:role="line"
|
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|
id="tspan3748-6"
|
||||||
|
style="fill:#999999;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
||||||
|
y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
|
||||||
|
<circle
|
||||||
|
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
|
||||||
|
id="path3663-1-4"
|
||||||
|
cx="18.004833"
|
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|
cy="90.979645"
|
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|
r="2.7302806" />
|
||||||
|
<circle
|
||||||
|
style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
|
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|
id="path3663-3-0-5"
|
||||||
|
cx="18.004833"
|
||||||
|
cy="81.949104"
|
||||||
|
r="2.7302806" />
|
||||||
|
<circle
|
||||||
|
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
|
||||||
|
id="path3663-6-6-2"
|
||||||
|
cx="18.004833"
|
||||||
|
cy="72.918564"
|
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|
r="2.7302806" />
|
||||||
|
<text
|
||||||
|
xml:space="preserve"
|
||||||
|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
|
||||||
|
x="6.9525447"
|
||||||
|
y="65.279381"
|
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|
id="text3707-5"><tspan
|
||||||
|
sodipodi:role="line"
|
||||||
|
id="tspan3705-4"
|
||||||
|
style="fill:#000000;stroke-width:0.264583"
|
||||||
|
x="6.9525447"
|
||||||
|
y="65.279381">$write(\{b\})$:</tspan></text>
|
||||||
|
<text
|
||||||
|
xml:space="preserve"
|
||||||
|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
|
||||||
|
x="59.340172"
|
||||||
|
y="118.94403"
|
||||||
|
id="text3707-5-3"><tspan
|
||||||
|
sodipodi:role="line"
|
||||||
|
id="tspan3705-4-6"
|
||||||
|
style="fill:#000000;stroke-width:0.264583"
|
||||||
|
x="59.340172"
|
||||||
|
y="118.94403">$read()$:</tspan></text>
|
||||||
|
<text
|
||||||
|
xml:space="preserve"
|
||||||
|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
||||||
|
y="75.619804"
|
||||||
|
id="text3750-7"><tspan
|
||||||
|
sodipodi:role="line"
|
||||||
|
id="tspan3748-4"
|
||||||
|
style="fill:#999999;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
||||||
|
y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text>
|
||||||
|
<text
|
||||||
|
xml:space="preserve"
|
||||||
|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
||||||
|
y="84.598038"
|
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|
id="text3750-3-4"><tspan
|
||||||
|
sodipodi:role="line"
|
||||||
|
id="tspan3748-2-3"
|
||||||
|
style="fill:#000000;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
||||||
|
y="84.598038">$\sqsupseteq \{b\} \to$ OK</tspan></text>
|
||||||
|
<text
|
||||||
|
xml:space="preserve"
|
||||||
|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
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|
y="93.54969"
|
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|
id="text3750-0-0"><tspan
|
||||||
|
sodipodi:role="line"
|
||||||
|
id="tspan3748-6-7"
|
||||||
|
style="fill:#999999;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
||||||
|
y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
|
||||||
|
<circle
|
||||||
|
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
|
||||||
|
id="path3663-6"
|
||||||
|
cx="118.63729"
|
||||||
|
cy="67.630196"
|
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|
r="2.7302806" />
|
||||||
|
<circle
|
||||||
|
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
|
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|
id="path3663-6-6-0"
|
||||||
|
cx="67.201363"
|
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|
cy="124.91125"
|
||||||
|
r="2.7302806" />
|
||||||
|
<text
|
||||||
|
xml:space="preserve"
|
||||||
|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
|
||||||
|
x="72.653946"
|
||||||
|
y="127.6125"
|
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|
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|
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|
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|
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|
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|
xml:space="preserve"
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|
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|
x="176.20593"
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|
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id="text1009-7"><tspan
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id="tspan1007-5"
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|
style="fill:#000000;stroke-width:0.264583"
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|
x="176.20593"
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|
y="67.008698">$\{c\}$</tspan></text>
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|
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|
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|
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|
id="g1183"
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|
transform="translate(51.996784,1.0317046)"
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|
style="fill:#000000">
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|
<text
|
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|
xml:space="preserve"
|
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|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
|
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|
x="112.90984"
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|
y="40.841526"
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id="text1117"><tspan
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id="tspan1115"
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|
style="fill:#000000;stroke-width:0.264583"
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|
x="112.90984"
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|
y="40.841526">$\{a,c\}$</tspan></text>
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||||||
|
<text
|
||||||
|
xml:space="preserve"
|
||||||
|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
|
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|
x="49.27084"
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|
y="40.841526"
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id="text1117-3"><tspan
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|
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id="tspan1115-5"
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style="fill:#000000;stroke-width:0.264583"
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|
x="49.27084"
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|
y="40.841526">$\{a,b\}$</tspan></text>
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|
<text
|
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|
xml:space="preserve"
|
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|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
|
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|
x="176.20593"
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|
y="40.841526"
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id="text1117-6"><tspan
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|
style="fill:#000000;stroke-width:0.264583"
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|
x="176.20593"
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|
y="40.841526">$\{b,c\}$</tspan></text>
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|
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|
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|
d="M 153.33622,90.367682 118.34198,73.428915"
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id="path1300" />
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|
<path
|
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|
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
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|
d="M 177.46016,90.367682 212.4544,73.428915"
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id="path1300-2" />
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|
<path
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|
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id="path1300-2-6" />
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<path
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<path
|
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sodipodi:nodetypes="cc" />
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|
sodipodi:nodetypes="cc" />
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|
<path
|
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|
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
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|
sodipodi:nodetypes="cc" />
|
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|
<path
|
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|
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
|
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|
d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
|
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|
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sodipodi:nodetypes="cc" />
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|
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||||||
|
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|
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|
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|
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cy="95.24971"
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|
<circle
|
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|
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|
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|
cx="176.97627"
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|
cy="68.155472"
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|
r="2.7302806" />
|
||||||
|
<circle
|
||||||
|
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
|
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|
id="path3663-1"
|
||||||
|
cx="18.004833"
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|
cy="39.402473"
|
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|
r="2.7302806" />
|
||||||
|
<circle
|
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|
style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
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|
id="path3663-3-0"
|
||||||
|
cx="18.004833"
|
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|
cy="30.371933"
|
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|
r="2.7302806" />
|
||||||
|
<circle
|
||||||
|
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
|
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|
id="path3663-6-6"
|
||||||
|
cx="18.004833"
|
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|
cy="21.341394"
|
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|
r="2.7302806" />
|
||||||
|
<text
|
||||||
|
xml:space="preserve"
|
||||||
|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
|
||||||
|
x="6.9525447"
|
||||||
|
y="13.702217"
|
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|
id="text3707"><tspan
|
||||||
|
sodipodi:role="line"
|
||||||
|
id="tspan3705"
|
||||||
|
style="fill:#000000;stroke-width:0.264583"
|
||||||
|
x="6.9525447"
|
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|
y="13.702217">$write(\{a\})$:</tspan></text>
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|
<text
|
||||||
|
xml:space="preserve"
|
||||||
|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
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|
y="24.042637"
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|
id="text3750"><tspan
|
||||||
|
sodipodi:role="line"
|
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|
id="tspan3748"
|
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|
style="fill:#000000;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
||||||
|
y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
|
||||||
|
<text
|
||||||
|
xml:space="preserve"
|
||||||
|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
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|
y="33.02087"
|
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|
id="text3750-3"><tspan
|
||||||
|
sodipodi:role="line"
|
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|
id="tspan3748-2"
|
||||||
|
style="fill:#999999;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
||||||
|
y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
|
||||||
|
<text
|
||||||
|
xml:space="preserve"
|
||||||
|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
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|
y="41.972523"
|
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|
id="text3750-0"><tspan
|
||||||
|
sodipodi:role="line"
|
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|
id="tspan3748-6"
|
||||||
|
style="fill:#999999;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
||||||
|
y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
|
||||||
|
<circle
|
||||||
|
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
|
||||||
|
id="path3663-1-4"
|
||||||
|
cx="18.004833"
|
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|
cy="90.979645"
|
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|
r="2.7302806" />
|
||||||
|
<circle
|
||||||
|
style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
|
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|
id="path3663-3-0-5"
|
||||||
|
cx="18.004833"
|
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|
cy="81.949104"
|
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|
r="2.7302806" />
|
||||||
|
<circle
|
||||||
|
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
|
||||||
|
id="path3663-6-6-2"
|
||||||
|
cx="18.004833"
|
||||||
|
cy="72.918564"
|
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|
r="2.7302806" />
|
||||||
|
<text
|
||||||
|
xml:space="preserve"
|
||||||
|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
|
||||||
|
x="6.9525447"
|
||||||
|
y="65.279381"
|
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|
id="text3707-5"><tspan
|
||||||
|
sodipodi:role="line"
|
||||||
|
id="tspan3705-4"
|
||||||
|
style="fill:#000000;stroke-width:0.264583"
|
||||||
|
x="6.9525447"
|
||||||
|
y="65.279381">$write(\{b\})$:</tspan></text>
|
||||||
|
<text
|
||||||
|
xml:space="preserve"
|
||||||
|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
|
||||||
|
x="59.340172"
|
||||||
|
y="118.94403"
|
||||||
|
id="text3707-5-3"><tspan
|
||||||
|
sodipodi:role="line"
|
||||||
|
id="tspan3705-4-6"
|
||||||
|
style="fill:#000000;stroke-width:0.264583"
|
||||||
|
x="59.340172"
|
||||||
|
y="118.94403">$read()$:</tspan></text>
|
||||||
|
<text
|
||||||
|
xml:space="preserve"
|
||||||
|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
||||||
|
y="75.619804"
|
||||||
|
id="text3750-7"><tspan
|
||||||
|
sodipodi:role="line"
|
||||||
|
id="tspan3748-4"
|
||||||
|
style="fill:#999999;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
||||||
|
y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text>
|
||||||
|
<text
|
||||||
|
xml:space="preserve"
|
||||||
|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
||||||
|
y="84.598038"
|
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|
id="text3750-3-4"><tspan
|
||||||
|
sodipodi:role="line"
|
||||||
|
id="tspan3748-2-3"
|
||||||
|
style="fill:#000000;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
||||||
|
y="84.598038">$\sqsupseteq \{b\} \to$ OK</tspan></text>
|
||||||
|
<text
|
||||||
|
xml:space="preserve"
|
||||||
|
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
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|
y="93.54969"
|
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|
id="text3750-0-0"><tspan
|
||||||
|
sodipodi:role="line"
|
||||||
|
id="tspan3748-6-7"
|
||||||
|
style="fill:#999999;stroke-width:0.264583"
|
||||||
|
x="23.457415"
|
||||||
|
y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
|
||||||
|
<circle
|
||||||
|
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
|
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|
id="path3663-6"
|
||||||
|
cx="118.63729"
|
||||||
|
cy="67.630196"
|
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|
r="2.7302806" />
|
||||||
|
<circle
|
||||||
|
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
|
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|
id="path3663-6-6-0"
|
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|
cx="67.201363"
|
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