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

摘要

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 E, 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 Cerny, and Restivo's conjecture on the minimal uncompletable word.