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On the State Complexity of Partial Derivative Automata For Regular Expressions with Intersection

  • Rafaela Bastos
  • Sabine Broda
  • António Machiavelo
  • Nelma MoreiraEmail author
  • Rogério Reis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9777)

Abstract

Extended regular expressions (with complement and intersection) are used in many applications due to their succinctness. In particular, regular expressions extended with intersection only (also called semi-extended) can already be exponentially smaller than standard regular expressions or equivalent nondeterministic finite automata (NFA). For practical purposes it is important to study the average behaviour of conversions between these models. In this paper, we focus on the conversion of regular expressions with intersection to nondeterministic finite automata, using partial derivatives and the notion of support. First, we give a tight upper bound of \(2^{O(n)}\) for the worst-case number of states of the resulting partial derivative automaton, where n is the size of the expression. Using the framework of analytic combinatorics, we then establish an upper bound of \((1.056 +o(1))^n\) for its asymptotic average-state complexity, which is significantly smaller than the one for the worst case.

Keywords

Regular Expression Real Zero Analytic Combinatorics Positive Zero Average Complexity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© IFIP International Federation for Information Processing 2016

Authors and Affiliations

  • Rafaela Bastos
    • 1
  • Sabine Broda
    • 1
  • António Machiavelo
    • 1
  • Nelma Moreira
    • 1
    Email author
  • Rogério Reis
    • 1
  1. 1.CMUP and Faculdade de Ciências da Universidade do PortoPortoPortugal

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