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Alphabetical Satisfiability Problem for Trace Equations
L. Breveglieri, A. Cherubini, C. Nuccio, and E. Rodaro
Abstract (in LaTeX format)
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.
Kewords: free partially commutative monoid, trace equation, NP-complete problem.
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BibTeX entry
@article{Breveglieri:2009:ActaCybernetica,author = {L. Breveglieri and A. Cherubini and C. Nuccio and E. Rodaro},
title = {Alphabetical Satisfiability Problem for Trace Equations},
journal = {Acta Cybernetica},
volume = {19},
number= {2},
pages = {479--497},
year = {2009},
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.},
keywords = {free partially commutative monoid, trace equation, NP-complete problem}
}