Solutions of word equations over partially commutative structures
conference contributionposted on 22.02.2018 by Volker Diekert, Artur Jez, Manfred Kufleitner
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© Volker Diekert, Artur Jez, and Manfred Kufleitner. We give NSPACE(n log n) algorithms solving the following decision problems. Satisfiability: Is the given equation over a free partially commutative monoid with involution (resp. a free partially commutative group) solvable? Finiteness: Are there only finitely many solutions of such an equation? PSPACE algorithms with worse complexities for the first problem are known, but so far, a PSPACE algorithm for the second problem was out of reach. Our results are much stronger: Given such an equation, its solutions form an EDT0L language effectively representable in NSPACE(n log n). In particular, we give an effective description of the set of all solutions for equations with constraints in free partially commutative monoids and groups.
Artur Jez was supported by a return fellowship of the Alexander von Humboldt Foundation. Manfred Kufleitner was supported by the grants DI 435/5-2 and KU 2716/1-1 of the DFG.
- Computer Science