In[]:=
FindLifetime[list_]:=If[#Length[list],None,#]&[First[FirstPosition[list,Last[list]]]]
s=2, k=1
s=2, k=1
In[]:=
ResourceFunction["ParallelMapMonitored"][FindLifetime[Length/@With[{t=6},MultiwayTuringMachine[#,{{1,t+1,0},Table[0,2t+1]},t]]]&,DeleteCases[Subsets[List/@TMRuleCases[2,1]],{}]]
Out[]=
{1,1,1,1,1,1,1,1,None,None,None,None,None,None,None,None,None,None,None,None,None,2,None,2,None,None,2,None,None,None,1,1,1,1,1,1,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,1,1,1,1,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,1,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None}
s=1, k=2
s=1, k=2
In[]:=
res12a=ResourceFunction["ParallelMapMonitored"][TimeConstrained[FindLifetime[Length/@With[{t=8},MultiwayTuringMachine[#,{{1,t+1,0},Table[0,2t+1]},t]]],2]&,DeleteCases[Subsets[List/@TMRuleCases[1,2]],{}]];
In[]:=
Max[res12a]
Out[]=
Max[1,None,$Aborted]
In[]:=
res12a=ResourceFunction["ParallelMapMonitored"][FindLifetime[Length/@With[{t=6},MultiwayTuringMachine[#,{{1,t+1,0},Table[0,2t+1]},t]]]&,DeleteCases[Subsets[List/@TMRuleCases[1,2]],{}]];
In[]:=
Max[res12a]
Out[]=
Max[1,None]
s=1, k=3
s=1, k=3
In[]:=
ResourceFunction["ParallelMapMonitored"][FindLifetime[Length/@With[{t=6},MultiwayTuringMachine[#,{{1,t+1,0},Table[0,2t+1]},t]]]&,DeleteCases[Subsets[List/@TMRuleCases[1,3]],{}]];
Max[%]
In[]:=
Length[DeleteCases[Subsets[List/@TMRuleCases[1,3]],{}]]
Out[]=
262143
s=2, k=2
s=2, k=2
ResourceFunction["ParallelMapMonitored"][FindLifetime[Length/@With[{t=6},MultiwayTuringMachine[#,{{1,t+1,0},Table[0,2t+1]},t]]]&,DeleteCases[Subsets[List/@TMRuleCases[2,2],{2}],{}]]
Out[]=
{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,None,None,None,None,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,None,None,None,None,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,None,None,None,None,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,None,None,None,None,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,None,None,None,None,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,None,None,None,None,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,None,None,None,None,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,None,None,None,None,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,None,None,None,None,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,None,None,None,None,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,None,None,None,None,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,None,None,None,None,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,None,None,None,None,2,2,2,2,1,1,1,1,1,1,1,1,1,1,None,None,None,None,2,2,2,2,1,1,1,1,1,1,1,1,1,None,None,None,None,2,2,2,2,1,1,1,1,1,1,1,1,None,None,None,None,2,2,2,2,1,1,1,1,1,1,1,1,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,2,2,2,None,None,3,3,None,None,3,3,2,2,None,None,4,2,None,None,None,None,2,3,3,None,None,3,3,None,None,4,2,None,None,None,None,None,None,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
In[]:=
ResourceFunction["ParallelMapMonitored"][FindLifetime[Length/@With[{t=6},MultiwayTuringMachine[#,{{1,t+1,0},Table[0,2t+1]},t]]]&,Select[DeleteCases[Subsets[List/@TMRuleCases[2,2],{2}],{}],Not@*TestDeterministic]]
Out[]=
{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
In[]:=
Max[%183]
Out[]=
Max[4,None]
In[]:=
Extract[DeleteCases[Subsets[List/@TMRuleCases[2,2],{2}],{}],Position[%183,4]]
Out[]=
{{{{1,0}{2,0,-1}},{{2,0}{1,1,1}}},{{{1,0}{2,0,1}},{{2,0}{1,1,-1}}}}
In[]:=
TMAppliesGraph[#,6]&/@%186
Out[]=
,
In[]:=
TuringMachinePlot[Flatten[#],2,2,"RulePlot"]&/@%186
Out[]=
,
In[]:=
TMAppliesStatesGraph[#,2,2,6]&/@%186
Out[]=
,
In[]:=
ResourceFunction["ParallelMapMonitored"][FindLifetime[Length/@With[{t=6},MultiwayTuringMachine[#,{{1,t+1,0},Table[0,2t+1]},t]]]&,DeleteCases[Subsets[List/@TMRuleCases[2,2],{3}],{}]]
In[]:=
Max[%]
Out[]=
Max[6,None]
In[]:=
Extract[DeleteCases[Subsets[List/@TMRuleCases[2,2],{3}],{}],Position[%196,6]]
Out[]=
{{{{1,1}{2,1,-1}},{{1,0}{2,1,1}},{{2,0}{1,1,-1}}},{{{1,1}{2,0,-1}},{{1,0}{2,1,1}},{{2,0}{1,1,-1}}},{{{1,1}{2,1,1}},{{1,0}{2,1,-1}},{{2,0}{1,1,1}}},{{{1,1}{2,0,1}},{{1,0}{2,1,-1}},{{2,0}{1,1,1}}},{{{2,1}{1,1,-1}},{{1,0}{2,1,1}},{{2,0}{2,1,-1}}},{{{2,1}{1,1,-1}},{{1,0}{2,1,1}},{{2,0}{2,0,-1}}},{{{2,1}{1,1,1}},{{1,0}{2,1,-1}},{{2,0}{2,1,1}}},{{{2,1}{1,1,1}},{{1,0}{2,1,-1}},{{2,0}{2,0,1}}},{{{2,1}{2,1,-1}},{{1,0}{2,0,-1}},{{2,0}{1,1,1}}},{{{2,1}{2,1,1}},{{1,0}{2,0,1}},{{2,0}{1,1,-1}}}}
NOTE: some missing.....
NOTE: this was still with p=5 !!!
This is the case for t=10: