Peg-solitaire, string rewriting systems and finite automata

Authors:
B. Ravikumar
Affiliations:
Department of Computer Science, Sonoma State University, 1801 East Cotati Av., Rohnert Park, CA
Venue:
Theoretical Computer Science
Year:
2004

Citing 5
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Abstract

We consider a class of length-preserving string rewriting systems and show that the set of encodings of pairs of strings 〈s, f〉 such that f can be derived from s using the rewriting rules can be accepted by finite automata. As a consequence, we show the existence of a linear time algorithm for determining the solvability of a given k × n peg-solitaire board, for any fixed k. This result is in contrast to the results of (13) and (1) that the same problem is NP-hard for n × n boards. We look at some related string rewriting systems and find conditions under which the encodings of the pairs 〈s,f〉 where f can be derived from s is regular.