The Existential Theory of Equations with Rational Constraints in Free Groups is PSPACEComplete
Abstract
It 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 PSPACEcomplete. We obtain this result as a corollary of the corresponding statement about free monoids with involution.
 Publication:

arXiv eprints
 Pub Date:
 March 2001
 arXiv:
 arXiv:cs/0103018
 Bibcode:
 2001cs........3018D
 Keywords:

 Computer Science  Data Structures and Algorithms;
 Computer Science  Logic in Computer Science;
 F.2.2;
 F.4
 EPrint:
 45 pages. LaTeX source