By Mazurov V.D.
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Additional resources for 2-groups with an odd-order automorphism that is the identity on involutions
If all the intersections in line (4) are finite sets, then one can compute the values k(t, q, s,p) from line (8). Therefore, we have an algorithm. Let us say a few words about its correctness. If in line (4) the intersection L(t, q) n£(£(s,p)) is infinite for some t,q,s,p £ Q and (q, s) £ S, then there are arbitrarily many strings z = uvx£,(v)y £ L with v £ L(t,q) and £(v) £ L(s,p), which implies that L is not loop-free. Remember that the automaton is minimal so that there must exist a path, empty or not, from go to t as well as one from p to a state in F.
An involution over a set S is a bijective mapping
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