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We investigate the complexity of algorithmic problems on finitely generated subgroups of free groups. Margolis and Meakin showed how a finite monoid Synt(H) can be canonically and effectively associated with such a subgroup H. We show that H is pure (that is, closed under radical) if and only if Synt(H) is aperiodic. We also show that testing for this… (More)

Birget, J.-C., SW. Margolis and J.C. Meakin, The word problem for inverse monoids presented by one idempotent relator, Theoretical Computer Science 123 (1994) 2733289. We study inverse monoids presented by a finite set of generators and one relation e= I, where e is a word representing an idempotent in the free inverse monoid, and 1 is the empty word. We… (More)

It is known that the problem of determining consistency of a finite system of equations in a free group or a free monoid is decidable, but the corresponding problem for systems of equations in a free inverse monoid of rank at least two is undecidable. Any solution to a system of equations in a free inverse monoid induces a solution to the corresponding… (More)

We prove that the word problem for the free product with amalgamation S U T of monoids can be undecidable, even when S and T are nitely presented monoids with word problems that are decidable in linear time, the factorization problems for U in each of S and T , as well as other problems, are decidable in polynomial time, and U is a free nitely generated… (More)

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