Solutions of Word Equations Over Partially Commutative Structures
نویسندگان
چکیده
We give NSPACE(n logn) 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 manysolutions of such an equation? PSPACE algorithms with worse complexities for the first problemare known, but so far, a PSPACE algorithm for the second problem was out of reach. Our resultsare much stronger: Given such an equation, its solutions form an EDT0L language effectivelyrepresentable in NSPACE(n logn). In particular, we give an effective description of the set ofall solutions for equations with constraints in free partially commutative monoids and groups.
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تاریخ انتشار 2016