Solutions of Word Equations Over Partially Commutative Structures
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.
Word equations
EDT0L language
trace monoid
right-angled Artin group
partial commutation
127:1-127:14
Regular Paper
Volker
Diekert
Volker Diekert
Artur
Jez
Artur Jez
Manfred
Kufleitner
Manfred Kufleitner
10.4230/LIPIcs.ICALP.2016.127
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