State Complexity of Prefix Distance of Subregular Languages

  • Timothy Ng
  • David Rappaport
  • Kai SalomaaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9777)


The neighbourhood of a regular language of constant radius with respect to the prefix distance is always regular. We give upper bounds and matching lower bounds for the size of the minimal deterministic finite automaton (DFA) needed for the radius k prefix distance neighbourhood of an n state DFA that recognizes, respectively, a finite, a prefix-closed and a prefix-free language. For prefix-closed languages the lower bound automata are defined over a binary alphabet. For finite and prefix-free regular languages the lower bound constructions use an alphabet that depends on the size of the DFA and it is shown that the size of the alphabet is optimal.


State Complexity Regular Language Empty String Deterministic Finite Automaton State Complexity Bound 
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© IFIP International Federation for Information Processing 2016

Authors and Affiliations

  1. 1.School of ComputingQueen’s UniversityKingstonCanada

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