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ResourceFunction["WolframModel"][{{1,2},{2,3}}{{1,3}},{{1,2},{2,3},{2,4}},Infinity]["ExpressionsEventsGraph",VertexLabelsAutomatic]
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This is just the causal graph, but with its edges labeled by expressions....
This is just the causal graph, but with its edges labeled by expressions....
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ResourceFunction["WolframModel"][{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}},Automatic,5]["LayeredCausalGraph"]
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Strings Analogs
Strings Analogs
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ResourceFunction["MultiwayEvolutionPlot"][{"BA""AB"},"BBBAAAA",4]
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ResourceFunction["MultiwayEvolutionPlot"][{"BA""AB"},"BBBAAAA",4,"EvolutionEventRendering""PositionalPolygons"]
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Local Multiway
Local Multiway
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ResourceFunction["WolframModel"][{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}},Automatic,2,"EventSelectionFunction"None]["ExpressionsEventsGraph",AspectRatio1/2,VertexSize5]
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ResourceFunction["WolframModel"][{{x,y}}{{y,z},{z,x}},Automatic,6,"EventSelectionFunction"None]["ExpressionsEventsGraph",AspectRatio1/2]
A splitting at an expression vertex is “a branching” [leading to branchlike separation]
A splitting at an event vertex [leading to spacelike separation]
A splitting at an expression vertex is “a branching” [leading to branchlike separation]
A splitting at an event vertex [leading to spacelike separation]
A splitting at an event vertex [leading to spacelike separation]
Test for branchlike vs spacelike separation: most recent common ancestor is expression vs. event vertex
Test for branchlike vs spacelike separation: most recent common ancestor is expression vs. event vertex
[Rulial separation: common ancestor is an expression vertex whose successor events correspond to different rules]
[Rulial separation: common ancestor is an expression vertex whose successor events correspond to different rules]
What is the analog of a branchial graph? What is the analog of a spatial graph?
What is the analog of a branchial graph? What is the analog of a spatial graph?
Spatial graph = a possible maximal collection of spacelike separated expressions.
Spatial graph = a possible maximal collection of spacelike separated expressions.
Given a set of expressions....
Given a set of expressions....
They have binary relations: separation is: timelike, spacelike, branchlike
We can also just measure the {b,t,x} distances
Turing machine case
Turing machine case