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22 + 11 rules, with 2 symbols

In[]:=
rules22=Catenate[Outer[Rule,Tuples[{1,0},2],Tuples[{1,0},2],1]]
Out[]=
In[]:=
ParallelMapMonitored[Labeled[TimeConstrained[MultiwaySystem[{#,{1}{0}},{{0,1,1,0,1,0,0}},7,"StatesGraphStructure"],5],#]&,rules22]
Out[]=
In[]:=
ParallelMapMonitored[Labeled[TimeConstrained[MultiwaySystem[{#,{1}{0}},{{0,1,1,0,0}},3,"StatesGraph"],5],#]&,rules22]
Out[]=

Causal Invariance

In[]:=
rules22
Out[]=
In[]:=
CausallyInvariantQ[{#},{{0,1,1,0,1,0,0}},7]&/@rules22
Out[]=
{True,True,True,True,True,True,True,True,True,True,True,True,True,True,True,True}
In[]:=
CausallyInvariantQ[{#},{{0,1,1,0,1,0,0}},10]&/@rules22
Out[]=
{True,True,True,True,True,True,True,True,True,True,True,True,True,True,True,True}
In[]:=
CausallyInvariantQ[{#,{1}{0}},{{0,1,1,0,1,0,0}},10]&/@rules22
Out[]=
{True,True,True,True,True,True,True,True,True,True,True,True,False,False,False,True}
In[]:=
CausallyInvariantQ[{"A""AB","B""A"},{"A"},5]
Out[]=
True
In[]:=
MultiwaySystem[{"A""AB","B""A"},{"A"},5,"CausalGraphStructure"]
Out[]=
In[]:=
MultiwaySystem[{{1,1}{0,1},{1}{0}},{{0,1,1,0,1,0,0}},5,"EvolutionCausalGraphStructure"]
Out[]=

Ensemble Evolution

Sorting

Do the eigenvectors have to be real?? (? Is it always a symmetric matrix? )
When is the evolution matrix unitary??
Independent regions of state space exist: cf conservation laws.

Non-causal invariant

Separating possible causal graphs

Filter out state nodes; event nodes only

Causal invariance case

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