In[]:=
ResourceFunction["WolframModel"][{{1,2},{2,3}}{{1,3}},{{1,2},{2,3},{2,4}},Infinity]["ExpressionsEventsGraph",VertexLabelsAutomatic]
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In[]:=
ResourceFunction["WolframModel"][{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}},Automatic,3]["ExpressionsEventsGraph",VertexLabelsAutomatic]
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This is just the causal graph, but with its edges labeled by expressions....

In[]:=
ResourceFunction["WolframModel"][{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}},Automatic,5]["ExpressionsEventsGraph"]
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In[]:=
ResourceFunction["WolframModel"][{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}},Automatic,5]["LayeredCausalGraph"]
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Strings Analogs

In[]:=
ResourceFunction["MultiwayEvolutionPlot"][{"BA""AB"},"BBBAAAA",4]
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ResourceFunction["MultiwayEvolutionPlot"][{"BA""AB"},"BBBAAAA",4,"EvolutionEventRendering""PositionalPolygons"]
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Local Multiway

In[]:=
ResourceFunction["WolframModel"][{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}},Automatic,2,"EventSelectionFunction"None]["ExpressionsEventsGraph",VertexLabelsAutomatic]
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In[]:=
ResourceFunction["WolframModel"][{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}},Automatic,1,"EventSelectionFunction"None]["ExpressionsEventsGraph",VertexLabelsAutomatic]
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In[]:=
ResourceFunction["WolframModel"][{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}},Automatic,2,"EventSelectionFunction"None]["ExpressionsEventsGraph",AspectRatio1/2,VertexSize5]
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A splitting at an expression vertex is “a branching” [leading to branchlike 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

[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?

Spatial graph = a possible maximal collection of spacelike separated 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