Alphabetical satisfiability problem for trace equations

Authors:
L. Breveglieri;A. Cherubini;C. Nuccio;E. Rodaro
Affiliations:
PoIitecnico di Milano, Department of Electronics and Information, Milano, Italy;Politecnico di Milano, Department of Mathematics, Milano, Italy;Politecnico di Milano, Department of Mathematics, Milano, Italy;Universitá dell'Insubria, DSCPI, Como, Italy
Venue:
Acta Cybernetica
Year:
2009

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Abstract

It is known that the satisfiability problem for equations over free partially commutative monoids is decidable but computationally hard. In this paper we consider the satisfiability problem for equations over free partially commutative monoids under the constraint that the solution is a subset of the alphabet. We prove that this problem is NP-complete for quadratic equations and that its uniform version is NP-complete for linear equations.