The Existential Theory of Equations with Rational Constraints in Free Groups is PSPACE-Complete

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dc.creatorDiekert, Volker
dc.creatorGutierrez, Claudio
dc.creatorHagenah, Christian
dc.date2001-03-26
dc.date.accessioned2026-07-07T03:17:01Z
dc.date.available2026-07-07T03:17:01Z
dc.descriptionIt is known that the existential theory of equations in free groups is decidable. This is a famous result of Makanin. On the other hand it has been shown that the scheme of his algorithm is not primitive recursive. In this paper we present an algorithm that works in polynomial space, even in the more general setting where each variable has a rational constraint, that is, the solution has to respect a specification given by a regular word language. Our main result states that the existential theory of equations in free groups with rational constraints is PSPACE-complete. We obtain this result as a corollary of the corresponding statement about free monoids with involution.
dc.description45 pages. LaTeX source
dc.identifierhttps://arxiv.org/abs/cs/0103018
dc.identifierhttp://arxiv.org/abs/cs/0103018
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/30571
dc.subjectData Structures and Algorithms
dc.subjectLogic in Computer Science
dc.subjectF.2.2; F.4
dc.titleThe Existential Theory of Equations with Rational Constraints in Free Groups is PSPACE-Complete
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