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

Mechanical proving with Walnut for squares and cubes in partial words