Deciding representability of sets of words of equal length

Authors:
Francine Blanchet-Sadri;Sean Simmons
Affiliations:
Department of Computer Science, University of North Carolina, Greensboro, NC;Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA
Venue:
DCFS'12 Proceedings of the 14th international conference on Descriptional Complexity of Formal Systems
Year:
2012

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Deciding representability of sets of words of equal length

Theoretical Computer Science

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Abstract

Partial words are sequences over a finite alphabet that may have holes that match, or are compatible with, all letters in the alphabet; partial words without holes are simply words. Given a partial word w, we denote by subw(n) the set of subwords of w of length n, i.e., words over the alphabet that are compatible with factors of w of length n. We call a set S of words h-representable if S=subw(n) for some integer n and partial word w with h holes. Using a graph theoretical approach, we show that the problem of whether a given set is h-representable can be decided in polynomial time. We also investigate other computational problems related to this concept of representability.