Multiway merging
Multiway merging
Lexicon
Lexicon
State: e.g. “ABAABB”: a state of the underlying substitution system.
Multistate: a collection of states e.g. at a particular step
No merging
No merging
Pure tree
Graph[MultiwaySystem[{"A""AA"},{"A"},2,"EvolutionTree"],VertexLabelsAutomatic]
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Graph[MultiwaySystem[{AAA},{A},2,EvolutionTree],VertexLabelsAutomatic]
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Graph[MultiwaySystem[{"A""AA"},{"A"},2,"EvolutionGraph"],VertexLabelsAutomatic]
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MultiwaySystem[{"A""ABA","B""A"},{"A"},3,"PredecessorRulesList"]
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{{A{}},{ABA{A}},{AAA{ABA},ABABA{ABA,ABA}},{AAABA{AAA,ABABA},AABAA{AAA},ABAAA{AAA,ABABA},ABABABA{ABABA,ABABA,ABABA}}}
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[[ Incorrect EvolutionTree ]]
[[ Incorrect EvolutionTree ]]
evoltree[list_]:=Graph[Flatten[{Style[#,Dotted]&/@Flatten[Module[{i=1},#{#,i++}&/@Flatten[Last/@#]]&/@list],Flatten[Map[Thread,list,{2}]]}]]
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evoltree[MultiwaySystem[{"A""ABA","B""A"},{"A"},3,"PredecessorRulesList"]]
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Module[{i=1},#{#,i++}&/@Flatten[Last/@#]]&/@MultiwaySystem[{"A""ABA","B""A"},{"A"},3,"PredecessorRulesList"]
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{{},{A{A,1}},{ABA{ABA,1},ABA{ABA,2},ABA{ABA,3}},{AAA{AAA,1},ABABA{ABABA,2},AAA{AAA,3},AAA{AAA,4},ABABA{ABABA,5},ABABA{ABABA,6},ABABA{ABABA,7},ABABA{ABABA,8}}}
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[We don’t have a causal graph for this case yet]
[We don’t have a causal graph for this case yet]
Merging of identical states at each step
Merging of identical states at each step
Graph[MultiwaySystem[{"A""AA","B""AB"},{"ABA"},2,"LayeredCausalGraph"],VertexLabelsAutomatic]
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Graph[MultiwaySystem[{"A""AA"},{"A"},3,"CausalGraph"],VertexLabelsAutomatic]
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Graph[MultiwaySystem[{"A""AA"},{"A"},3,"ElementwiseEvolutionCausalGraph"],VertexLabelsAutomatic]
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MultiwaySystem[{"A""AA"},{"A"},5,"CausalGraph"]
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MultiwaySystem[{"A""AA"},{"A"},6,"CausalGraph"]
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MultiwaySystem[{"A""AA"},{"A"},7,"CausalGraph"]
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Graph[MultiwaySystem[{"BA""AB"},{"BBAA"},5,"CausalGraph"],VertexLabelsAutomatic]
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Graph[MultiwaySystem[{"BA""AB"},{"BBAA"},5,"EvolutionCausalGraph"],VertexLabelsAutomatic]
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Graph[MultiwaySystem[{"BA""AB"},{"BBBAAA"},10,"EvolutionCausalGraph"],VertexLabelsAutomatic]
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LayeredGraphPlot[MultiwaySystem[{"BA""AB"},{"BBBAAA"},10,"EvolutionCausalGraph"],VertexLabelsAutomatic]
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MultiwaySystem[{"BA""AB"},{"BBBAAA"},10,"EvolutionPlot"]
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MultiwaySystem[{"BA""AB"},{"BBBAAA"},10,"EvolutionPlot","EventRendering""PositionalPolygons"]
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MultiwaySystem[{"BA""AB"},{"BBBAAA"},10,"CausalGraph"]
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Merging across all steps (traditional causal graph)
Merging across all steps (traditional causal graph)
Events list
Events list
Imagine automatic parallelization of all updating orders
Imagine automatic parallelization of all updating orders
I.e. run the multiway system with every path in the MW system being run on a different parallel processor
Non-multiway causal graph construction
Non-multiway causal graph construction
Labeled[SREvolutionGraphicsStreamed[SRXEvolveList[#,"AAABBB",6]],SRRuleGraphic[#]]&[{"AAB""ABBBAA"}]
SMWNetworkPictureR[{"AAB""ABBBAA"},"AAABBB",8,{0},RibbonTrue,RibbonColorTableLast/@$ColorMap,MaxLevel4,ArrowsTrue,NodeSize0.1,SymmetrizedTrue,NodeColorGray]
Relativity vs. QM
In the relationship between events, there can be timelike-separated events which affect each other through updates. There can be spacelike-separated events
There can be branch-separated events which arise from different rewrites of a single expression.
There can be branch-separated events which arise from different rewrites of a single expression.
To do list
Specification of events for naming nodes (to agree with “AllEventsList”)
Specification of events for naming nodes (to agree with “AllEventsList”)
Formatting of evolution causal graphs [ different vertex shapes ]
Formatting of evolution causal graphs [ different vertex shapes ]
Using actual strings as vertex shapes in various graphs
Using actual strings as vertex shapes in various graphs