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A symbolic finite-state approach for automated proving of theorems in combinatorial game theory. (English) Zbl 1232.91071

Summary: We develop a finite-state automata approach, implemented in a Maple package Toads and Frogs available from our websites, for conjecturing, and then rigorously proving, values for large families of positions in Richard Guy’s combinatorial game Toads and Frogs. In particular, we prove a conjecture of Jeff Erickson.

MSC:

91A46 Combinatorial games
68T15 Theorem proving (deduction, resolution, etc.) (MSC2010)

Software:

ToadsAndFrogs; Maple
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References:

[1] Berlekamp E., Winning Ways for your Mathematical Plays (1982) · Zbl 0485.00025
[2] Erickson J., Games of No Chance 29 pp 299– (1996)
[3] T. ”Aek” Thanatipanonda, Further hopping with toads and frogs, preprint (available from the author’s website)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.