## On the complexity of intersection and conjugacy problems in free groups.(English)Zbl 0555.20016

This paper is a continuation of the paper reviewed above. Like its predecessor, this paper is aimed very much at the computer scientist. From the authors’ abstract: ”Having a Nielsen reduced set of generators for subgroups H and K [of a free group F] one can solve a lot of intersection and conjugacy problems in polynomial time in a uniform way. We study the solvability of (i)$$\exists h\in H$$, $$k\in K:$$ $$hx=yk$$ in F, and (ii) $$\exists w\in F$$ $$w^{-1}Hw=K$$ and characterize the set of solutions. This leads for (i) to an algorithm for computing a set of generators for $$H\cap K$$ (and a new proof that free groups have the Howson property). For (ii) this gives a fast solution of Moldavanskij’s conjugacy problem; an algorithm for computing the normal hull of H then gives a representation of all solutions. All the algorithms run in polynomial time and the decision problems are proved to be P-complete under log-space reducibility”.
Reviewer: S.J.Pride

### MSC:

 20E05 Free nonabelian groups 20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)

Zbl 0555.20015
Full Text:

### References:

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