Reversibility

What makes a string rewriting system reversible?

"AB""BA"
If you go to the final state, and reverse the rule, can you get back? E.g. for sorting, if you just have a sorted output, there are many inputs that will lead to the same sorted output.

Cf effective reversibility of equilibrium in CAs

[Any state that isn’t going to survive is already gone]
In[]:=
Graph[#CellularAutomaton[30][#]&/@Tuples[{1,0},9]]
Out[]=
When is a states graph non-contractive?
In[]:=
MultiwaySystem[{{1,0}{0,1}},Tuples[{1,0},5],1,"StatesGraph"]
Out[]=
In[]:=
MultiwaySystem[{{1,0}{0,1}},Tuples[{1,0},5],1,"EvolutionEventsGraph"]
Out[]=
In[]:=
MultiwaySystem[{{1,0}{0,1}},Tuples[{1,0},5],1,"EvolutionCausalGraph"]
Out[]=