The Computational Complexity of Universality Problems for Prefixes, Suffixes, Factors, and Subwords of Regular Languages

Narad Rampersad
Jeffrey Shallit
Fundamenta Informaticae, 116(2012), pp. 223-236


In this paper we consider the computational complexity of the following problems: given a DFA or NFA representing a regular language L over a finite alphabet Σ, is the set of all prefixes (resp., suffixes, factors, subwords) of all words of L equal to Σ*? In the case of testing universality for factors of languages, there is a connection to two classic problems: the synchronizing words problem of Černý, and Restivo's conjecture on the minimal uncompletable word.

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