Mechanical proving with Walnut for squares and cubes in partial words

Abstract

Walnut is a software that using automata can prove theorems in combinatorics on words about automatic sequences. We are able to apply this software to both prove new results as well as reprove some old results on avoiding squares and cubes in partial words. We also define the notion of an antisquare in a partial word and begin the study of binary partial words which contain only a fixed number of distinct squares and antisquares.