A characterization of Thompson digraphs

  • Authors:

  • Dora Giammarresi;Jean-Luc Ponty;Derick Wood;Djelloul Ziadi

  • Affiliations:

  • Dipartimento di matematica, Universitá di Roma "Tor Vergata", via della ricerca scientifica, 00133 Rome, Italy;25 rue Philippe Lebon, BP 540, 76058 Le Havre Cedex, France;Department of Computer Science, Hong Kong University of Science & Technology, Clear Water Bay, Kowloon, Hong Kong, China;L.I.F.A.R. (Laboratoire d'Informatique), Université de Rouen, 76821 Mont-Saint-Aignan Cedex, France

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2004

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Abstract

A finite-state machine is called a Thompson machine if it can be constructed from an empty-free regular expression using the construction of Thompson as modified by Hopcroft and Ullman. We call the underlying digraph of a Thompson machine a Thompson digraph. We characterize Thompson digraphs and we give an algorithm that generates an equivalent regular expression from a Thompson machine that has size linear in the total number of states and transitions. Although the algorithm is simple, it is novel in that the usual constructions of equivalent regular expressions from finite-state machines produce regular expressions that have size exponential in the size of the given machine, in the worst case. The algorithm provides a tentative first step in the construction of small expressions from finite-state machines.