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Tree check: cycle-free , rooted tree.. #94

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Tree check: cycle-free , rooted tree.. #94

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19deb47
Tree check: cycle-free , rooted tree
Dec 24, 2023
324e71e
update Graphs.tla
Dec 29, 2023
fdafc72
Refine IsTreeWithRoot() definition for precise rooted tree semantics
younes-io Nov 11, 2024
690bd4b
fix: (simplified) tree definition typos
younes-io Nov 11, 2024
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15 changes: 11 additions & 4 deletions modules/Graphs.tla
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Expand Up @@ -61,11 +61,18 @@ IsStronglyConnected(G) ==
-----------------------------------------------------------------------------
IsTreeWithRoot(G, r) ==
/\ IsDirectedGraph(G)
/\ \A e \in G.edge : /\ e[1] # r
/\ \A f \in G.edge : (e[1] = f[1]) => (e = f)
/\ \A n \in G.node : AreConnectedIn(n, r, G)
/\ (Cardinality(G.node) = 1 => G.node = {r})
\* Handles single-node tree case
/\ \A n \in G.node \ {r} : \E! f \in G.edge : f[2] = n
\* Every node except the root has exactly one incoming edge
/\ \A n \in G.node \ {r} : AreConnectedIn(r, n, G)
\* Every node other than the root is reachable from the root
/\ \A n \in G.node \ {r} : ~\E path \in SimplePath(G) : path[1] = n /\ path[Len(path)] = n
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\* No cycles: No path from a node to itself

=============================================================================
\* Modification History
\* Last modified Sun Dec 24 14:31:00 CET 2023 by Younes Akhouayri
\* Last modified Sun Mar 06 18:10:34 CET 2022 by Stephan Merz
\* Last modified Tue Dec 21 15:55:45 PST 2021 by Markus Kuppe
\* Created Tue Jun 18 11:44:08 PST 2002 by Leslie Lamport
\* Created Tue Jun 18 11:44:08 PST 2002 by Leslie Lamport