State Complexity of Neighbourhoods and Approximate Pattern Matching

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9168)


The neighbourhood of a language L with respect to an additive distance consists of all strings that have distance at most the given radius from some string of L. We show that the worst case (deterministic) state complexity of a radius r neighbourhood of a language recognized by an n state nondeterministic finite automaton A is \((r+2)^n\). The lower bound construction uses an alphabet of size linear in n. We show that the worst case state complexity of the set of strings that contain a substring within distance r from a string recognized by A is \((r+2)^{n-2} + 1\).


Regular languages State complexity Lower bounds Additive distance 


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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.School of ComputingQueen’s UniversityKingstonCanada

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