Optimal Lower Bounds on Regular Expression Size Using Communication Complexity

  • Hermann Gruber
  • Jan Johannsen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4962)


The problem of converting deterministic finite automata into (short) regular expressions is considered. It is known that the required expression size is 2 Θ(n) in the worst case for infinite languages, and for finite languages it is n Ω(loglogn) and n O(logn), if the alphabet size grows with the number of states n of the given automaton. A new lower bound method based on communication complexity for regular expression size is developed to show that the required size is indeed n Θ(logn).

For constant alphabet size the best lower bound known to date is Ω(n 2), even when allowing infinite languages and nondeterministic finite automata. As the technique developed here works equally well for deterministic finite automata over binary alphabets, the lower bound is improved to n Ω(logn).


Regular Expression Communication Complexity Search Problem Regular Language Boolean Formula 
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

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Hermann Gruber
    • 1
  • Jan Johannsen
    • 1
  1. 1.Institut für InformatikMünchenGermany

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