Combinatorial Complexity of Regular Languages

  • Arseny M. Shur
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5010)


We study combinatorial complexity (or counting function) of regular languages, describing these functions in three ways. First, we classify all possible asymptotically tight upper bounds of these functions up to a multiplicative constant, relating each particular bound to certain parameters of recognizing automata. Second, we show that combinatorial complexity equals, up to an exponentially small term, to a function constructed from a finite number of polynomials and exponentials. Third, we describe oscillations of combinatorial complexity for factorial, prefix-closed, and arbitrary regular languages. Finally, we construct a fast algorithm for calculating the growth rate of complexity for regular languages, and apply this algorithm to approximate growth rates of complexity of power-free languages, improving all known upper bounds for growth rates of such languages.


Complexity Function Combinatorial Complexity Regular Language Counting Function Factorial Language 
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© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Arseny M. Shur
    • 1
  1. 1.Ural State University 

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