Relating the degree of ambiguity of finite automata to the succinctness of their representation

  • Oscar H. Ibarra
  • Bala Ravikumar
Session 1 Automata And Formal Languages
Part of the Lecture Notes in Computer Science book series (LNCS, volume 287)


We consider the problem of how the size of a nondeterministic finite automaton (nfa) representing a regular language depends on the degree of ambiguity of the nfa. We obtain results for the unary and bounded inputs, and partial results for the unrestricted inputs. One of the main results of this paper shows that for unrestricted inputs, deterministic, unambiguous and nondeterministic machines form a hierarchy with respect to the number of states, solving an open problem of Stearns and Hunt. We also propose a new approach to the study of the succinctness of representation through regularity preserving closure properties and obtain some results in this direction.


Regular Expression Start State Regular Language Finite Automaton Closure Property 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Oscar H. Ibarra
    • 1
  • Bala Ravikumar
    • 1
  1. 1.Department of Computer ScienceUniversity of MinnesotaMinneapolis

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