Automatic theorem-proving in combinatorics on words

Authors:
Daniel Goč;Dane Henshall;Jeffrey Shallit
Affiliations:
School of Computer Science, University of Waterloo, Waterloo, ON, Canada;School of Computer Science, University of Waterloo, Waterloo, ON, Canada;School of Computer Science, University of Waterloo, Waterloo, ON, Canada
Venue:
CIAA'12 Proceedings of the 17th international conference on Implementation and Application of Automata
Year:
2012

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Abstract

We describe a technique for mechanically proving certain kinds of theorems in combinatorics on words, using finite automata and a package for manipulating them. We illustrate our technique by applying it to (a) solve an open problem of Currie and Saari on the lengths of unbordered factors in the Thue-Morse sequence; (b) verify an old result of Prodinger and Urbanek on the paperfolding sequence and (c) find an explicit expression for the recurrence function for the Rudin-Shapiro sequence. All results were obtained by machine computations.