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 x n peg-solitaire board, for any fixed k. This result is in contrast to the recent results of [UEHA] and [AVIS] 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.
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© 1997 Springer-Verlag Berlin Heidelberg
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Ravikvmar, B. (1997). Peg-solitaire, string rewriting systems and finite automata. In: Leong, H.W., Imai, H., Jain, S. (eds) Algorithms and Computation. ISAAC 1997. Lecture Notes in Computer Science, vol 1350. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63890-3_26
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DOI: https://doi.org/10.1007/3-540-63890-3_26
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