On the Average Complexity of Strong Star Normal Form

  • Sabine Broda
  • António Machiavelo
  • Nelma Moreira
  • Rogério Reis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10316)


For regular expressions in (strong) star normal form a large set of efficient algorithms is known, from conversions into finite automata to characterisations of unambiguity. In this paper we study the average complexity of this class of expressions using analytic combinatorics. As it is not always feasible to obtain explicit expressions for the generating functions involved, here we show how to get the required information for the asymptotic estimates with an indirect use of the existence of Puiseux expansions at singularities. We study, asymptotically and on average, the alphabetic size, the size of the \(\varepsilon \)-follow automaton and the ratio of these expressions to standard regular expressions.


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Copyright information

© IFIP International Federation for Information Processing 2017

Authors and Affiliations

  • Sabine Broda
    • 1
  • António Machiavelo
    • 1
  • Nelma Moreira
    • 1
  • Rogério Reis
    • 1
  1. 1.CMUP & DM-DCC, Faculdade de Ciências da Universidade do PortoPortoPortugal

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