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

  • Authors:
  • Narad Rampersad;Jeffrey Shallit;Zhi Xu

  • Affiliations:
  • Department of Mathematics and Statistics, University of Winnipeg, 515 Portage Avenue, Winnipeg, Manitoba R3B 2E9, Canada, narad.rampersad@gmail.com;(Correspd.) School of Computer Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada, shallit@cs.uwaterloo.ca/ zxu@google.com;School of Computer Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada, shallit@cs.uwaterloo.ca/ zxu@google.com

  • Venue:
  • Fundamenta Informaticae - Words, Graphs, Automata, and Languages; Special Issue Honoring the 60th Birthday of Professor Tero Harju
  • Year:
  • 2012

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Abstract

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.