allsigs
In[]:=
Out[]=
EnumerateSubstitutionSystemRules[#,2]&/@Take[allsigs,5]
In[]:=
Out[]=
ParallelMapMonitored[#TimeConstrained[Do[If[TotalCausalInvariantQ[#,t],Return[t]],{t,7}],2]&,EnumerateSubstitutionSystemRules[Echo@#,2]]&/@Take[allsigs,20]
In[]:=
{11}
»
{12}
»
{13}
»
{22}
»
{11,11}
»
{14}
»
{23}
»
{11,12}
»
{11,21}
»
{15}
»
{24}
»
{33}
»
{11,13}
»
{11,31}
»
{11,22}
»
{12,12}
»
{12,21}
»
{11,11,11}
»
{16}
»
{25}
»
Out[]=
Position[%,2]
In[]:=
{{15,14,2},{17,4,2}}
Out[]=
%%[[15,14]]
In[]:=
{AB,ABAA}2
Out[]=
Length[allsigs]
In[]:=
59
Out[]=
ParallelMapMonitored[#TimeConstrained[Do[If[TotalCausalInvariantQ[#,t],Return[t]],{t,7}],2]&,EnumerateSubstitutionSystemRules[Echo@#,2]]&/@Drop[allsigs,20]
In[]:=
{34}
»
{11,14}
»
{11,41}
»
{11,23}
»
{11,32}
»
{12,13}
»
{12,31}
»
{13,21}
»
{12,22}
»
{21,22}
»
{11,11,12}
»
{11,11,21}
»
{17}
»
{26}
»
{35}
»
{11,15}
»
{11,51}
»
{44}
»
{11,24}
»
{11,42}
»
{12,14}
»
{12,41}
»
{14,21}
»
{11,33}
»
{13,13}
»
{13,31}
»
{12,23}
»
{12,32}
»
{13,22}
»
{21,23}
»
{22,31}
»
{11,11,13}
»
{11,11,31}
»
{22,22}
»
{11,11,22}
»
{11,12,12}
»
{11,12,21}
»
{11,21,21}
»
{11,11,11,11}
»
Out[]=
​
allres=Join[%131,%];
In[]:=

Full results:

allres=
If[
]
Byte count: 536
;
In[]:=
Syntax
:This input can only be interpreted in the same kernel session that generated it.
Cases[Level[allres,{-1}],Null|_Integer]
In[]:=
Out[]=
Counts[%]
In[]:=
11777,Null969,2142,326,410
Out[]=
FirstPosition[allres,2]
In[]:=
{15,14,2}
Out[]=
FirstPosition[allres,3]
In[]:=
{26,5,2}
Out[]=
FirstPosition[allres,4]
In[]:=
{41,8,2}
Out[]=
Length[allres]
In[]:=
59
Out[]=
Length[%139]
In[]:=
2924
Out[]=
allres[[15,14]]
In[]:=
{AB,ABAA}2
Out[]=
allres[[26,5]]
In[]:=
{AAA,ABAB}3
Out[]=
allres[[41,8]]
In[]:=
{AAA,ABAAB}4
Out[]=
MultiwaySystem[{"A""AA","A""BAAB"},"A",5,"StatesGraphStructure"]
In[]:=
Out[]=
{"AB""A","BA""BAA"}Null,{"AB""A","BA""BAB"}2
Values[11777,2142,326,410]
In[]:=
{1777,142,26,10}
Out[]=
Ratios[%]//N
In[]:=
{0.07991,0.183099,0.384615}
Out[]=
TotalCausalInvariantQ[{"A""B","AB""AA"},3]
In[]:=
True
Out[]=
TotalCausalInvariantQ[{"A""B","AB""AA"},1]
In[]:=
False
Out[]=
TotalCausalInvariantQ[{"A""B","AB""AA"},2]
In[]:=
True
Out[]=
Cases[Catenate[allres],(x_2)x]
In[]:=
Out[]=
findCanonicalCriticalPairs/@%
In[]:=
Out[]=
InteractiveListSelectorSW[MultiwaySystem[#,Flatten[findCanonicalCriticalPairs[#]],4,"StatesGraphStructure"]#&/@Cases[Catenate[allres],(x_2)x]]
In[]:=
Out[]=
findCanonicalCriticalPairs@{"A""AA","AB""BA"}
In[]:=
{{AAB,AAB},{AAB,BA},{BA,BA}}
Out[]=
LayeredGraphPlot[MultiwaySystem[#,Flatten@findCanonicalCriticalPairs[#],4,"StatesGraph"]]&/@{{"A""AAB","AA""A"},{"A""AA","AB""BA"},{"A""ABA","AAB""A"},{"A""BAB","AB""AA"}}
In[]:=
Out[]=
InteractiveListSelectorSW[MultiwaySystem[#,Flatten[findCanonicalCriticalPairs[#]],4,"StatesGraphStructure"]#&/@Cases[Catenate[allres],(x_4)x]]
In[]:=
Out[]=
Cases[Catenate[allres],(x_4)x]
In[]:=
{{AAA,ABAAB},{AAA,ABABB},{AAA,AAABB},{AAA,AABAB},{AAAAA,ABB},{ABAAB,AAA},{AAAA,ABAB},{AAA,AABAB},{AAAB,AABA},{AB,AAA,BBA}}
Out[]=
Labeled[LayeredGraphPlot[MultiwaySystem[#,Flatten@findCanonicalCriticalPairs[#],5,"StatesGraph"]],#]&/@%184
In[]:=
Out[]=
findCanonicalCriticalPairs[{"A""AA","AAAB""B"}]
In[]:=
{{AAAAB,AAAAB},{AAAAB,B},{B,B}}
Out[]=
LayeredGraphPlot[MultiwaySystem[{"A""AA","AAAB""B"},"AAAB",4,"StatesGraph"],"AAAB"Top]
In[]:=
Out[]=
findCanonicalCriticalPairs[{"A""B","A""AA","BB""A"}]
In[]:=
{{A,A},{AA,AA},{AA,B},{AB,AB},{AB,BA},{B,B},{BA,BA}}
Out[]=
LayeredGraphPlot[MultiwaySystem[{"A""B","A""AA","BB""A"},"A",4,"StatesGraph"],"A"Top]
In[]:=
Out[]=
TotalCausalInvariantQ[{"A""B","AAB""BAA"},1]
In[]:=
False
Out[]=
LayeredGraphPlot[MultiwaySystem[{"A""AA","A""BAB"},"AB",3,"StatesGraph"]]
In[]:=
Out[]=