Follow automata

  • Authors:

  • Lucian Ilie;Sheng Yu

  • Affiliations:

  • Department of Computer Science, University of Western Ontario, London, ON, Canada N6A 5B7;Department of Computer Science, University of Western Ontario, London, ON, Canada N6A 5B7

  • Venue:
  • Information and Computation
  • Year:
  • 2003

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Abstract

We give two new algorithms for constructing small nondeterministic finite automata (NFA) from regular expressions. The first constructs NFAs with ε-transitions (εNFA) which are smaller than all the other εNFAs obtained by similar constructions. Their size is at most 3/2 |α| + 5/2, where α is the regular expression. This is very close to optimal since we prove also the lower bound 4/3; |α| + 5/2. The second constructs NFAs. It uses ε-elimination in the εNFAs we just introduced and builds a quotient of the well-known position automaton w.r.t. the equivalence given by the follow relation; therefore giving the name of follow automaton. The new automaton uses optimally the information from the positions of a regular expression. We compare the follow automaton with the best constructions to date and show that it has important advantages over those.