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MultiwaySystem[{"A""AA"},"A",5,"StatesGraph"]
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MultiwaySystem[{"A""AB","A""AC"},"A",3,"StatesGraph"]
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Table[MultiwaySystem[{"A""AB","A""AC"},"A",t,"BranchialGraph"],{t,4}]
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MultiwaySystem[{"""A","""B"},"",3,"StatesGraph",GraphLayout->"LayeredDigraphEmbedding"]
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Table[MultiwaySystem[{"""A","""B"},"A",t,"BranchialGraph"],{t,4}]
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Graph3D
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Table[MultiwaySystem[{"""A","""B"},"",t,"BranchialGraph"],{t,4}]
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Connected to strings that can be reached by doing (inverse rule) * (rule)
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DeBruijnGraph[2,3,GraphLayout"SpringElectricalEmbedding",VertexLabelsAutomatic]
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DeBruijnGraph[2,2,GraphLayout"SpringElectricalEmbedding"]
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StringTuples["AB",3]
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{AAA,AAB,ABA,ABB,BAA,BAB,BBA,BBB}
Analogy to de Bruijn graphs
Analogy to de Bruijn graphs
Every critical pair is associated with an overlap in where the rule can be applied
Analogy with edit distance
Analogy with edit distance
Assume the edits are rule applications and inverse rule applications
Dimensions etc.
Dimensions etc.
Symmetry is broken like Pascal’s triangle....
Radius is always time step + 1
Radius is always time step + 1
Pure Tree Case
Pure Tree Case
Simpler Rules
Simpler Rules
To get between elements, you delete anywhere, and add anywhere. [Max degree ?? 2 length^2 ]
It is this, because you can add at the beginning or end....
A rule to be edit distance
A rule to be edit distance
Every move in the branchial graph is an operation, and an inverse operation
Every move in the branchial graph is an operation, and an inverse operation
Interpretation
Interpretation
What are the inertial frames??
What are the inertial frames??
Are there complex numbers in the distances between states?
Are there complex numbers in the distances between states?
Can we think about cosmological branchial distances as imaginary distances?
[ Spacelike, timelike, branchial : tagging distances by positive, negative, + something else ]
[ Spacelike, timelike, branchial : tagging distances by positive, negative, + something else ]
Fisher Information
Fisher Information
Ed Hypothesis
Ed Hypothesis