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.
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Goč, D., Henshall, D., Shallit, J. (2012). Automatic Theorem-Proving in Combinatorics on Words. In: Moreira, N., Reis, R. (eds) Implementation and Application of Automata. CIAA 2012. Lecture Notes in Computer Science, vol 7381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31606-7_16
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