Complexity of Makanin's algorithm
Journal of the ACM (JACM)
Makanin's algorithm is not primitive recursive
Theoretical Computer Science
Satisfiability of word equations with constants is in NEXPTIME
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Solving word equations modulo partial commutations
Theoretical Computer Science
Satisfiability of equations in free groups is in PSPACE
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
The expressibility of languages and relations by word equations
Journal of the ACM (JACM)
Automata, Languages, and Machines
Automata, Languages, and Machines
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
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LFCS '97 Proceedings of the 4th International Symposium on Logical Foundations of Computer Science
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ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Application of Lempel-Ziv Encodings to the Solution of Words Equations
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Equations in Free Semigroups with Anti-involution and Their Relation to Equations in Free Groups
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
Makanin's Algorithm for Word Equations - Two Improvements and a Generalization
IWWERT '90 Proceedings of the First International Workshop on Word Equations and Related Topics
Testing Equivalence of Morphisms on Context-Free Languages
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
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FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Satisfiability of Word Equations with Constants is in PSPACE
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Satisfiability of word equations with constants is in PSPACE
Journal of the ACM (JACM)
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It is well-known that the existential theory of equations in free groups is decidable. This is a celebrated result of Makanin which was published 1982. Makanin did not discuss complexity issues, but later it was shown that the scheme of his algorithm is not primitive recursive. In this paper we present an algorithm that works in polynomial space. This improvement is based upon an extension of Plandowski's techniques for solving word equations. We present a PSPACE-algorithm in a 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. We obtain our main result about the existential theory in free groups as a corollary of the corresponding statement in free monoids with involution.