Mathematical Analogs
Mathematical Analogs
https://www.wolframscience.com/nks/notes-5-6--semigroups-and-groups-and-multiway-systems/
https://www.wolframscience.com/nks/notes-5-6--semigroups-and-groups-and-multiway-systems/
Is a semigroup-emulating rewriting system causal invariant?
Potential proof: https://hal.archives-ouvertes.fr/hal-00455588/document
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MultiwaySystem[{"ABB""BA","BA""ABB"},{"AAAABA"},3,"CausalGraph"]
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CausallyInvariantQ[{"ABB""BA","BA""ABB"},{"AAAABA"},3]
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True
Claim: associativity of the reflexive transitive closure of the abstract replacement operation is equivalent to confluence
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MultiwaySystem[{"AB""BA","BA""AB"},{"AAAABA"},8,"EvolutionPlot"]
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The distinct elements e.g. of a semigroup
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MultiwaySystem[{"AB""BA","BA""AB"},{"AAAABA"},8,"StatesGraph"]
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MultiwaySystem[{"AB""BA","BA""AB"},{"ABBABA"},8,"StatesGraph"]
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MultiwaySystem[{"AB""BA","BA""AB"},{"ABBABA"},12,"StatesGraph"]
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MultiwaySystem[{"AB""BA","BA""AB"},{"AAABBB"},12,"StatesGraph"]
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Cayley graph comes when we are applying a concatenation operator to get to a potentially new element of the group, modding out by the multiway states graph associated with that new element.
Cayley graph comes when we are applying a concatenation operator to get to a potentially new element of the group, modding out by the multiway states graph associated with that new element.
Cayley graph represents a map of inequivalent initial conditions
Cayley graph represents a map of inequivalent initial conditions