On the Size Complexity of Deterministic Frequency Automata

  • Rūsiņš Freivalds
  • Thomas Zeugmann
  • Grant R. Pogosyan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7810)


Austinat, Diekert, Hertrampf, and Petersen [2] proved that every language L that is (m,n)-recognizable by a deterministic frequency automaton such that m > n/2 can be recognized by a deterministic finite automaton as well. First, the size of deterministic frequency automata and of deterministic finite automata recognizing the same language is compared. Then approximations of a language are considered, where a language L′ is called an approximation of a language L if L′ differs from L in only a finite number of strings. We prove that if a deterministic frequency automaton has k states and (m,n)-recognizes a language L, where m > n/2, then there is a language L′ approximating L such that L′ can be recognized by a deterministic finite automaton with no more than k states.

Austinat et al. [2] also proved that every language L over a single-letter alphabet that is (1,n)-recognizable by a deterministic frequency automaton can be recognized by a deterministic finite automaton. For languages over a single-letter alphabet we show that if a deterministic frequency automaton has k states and (1,n)-recognizes a language L then there is a language L′ approximating L such that L′ can be recognized by a deterministic finite automaton with no more that k states. However, there are approximations such that our bound is much higher, i.e., k!.


Frequency Computation Regular Language Input String Probabilistic Algorithm Chinese Remainder Theorem 
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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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Rūsiņš Freivalds
    • 1
    • 2
  • Thomas Zeugmann
    • 2
  • Grant R. Pogosyan
    • 3
  1. 1.Institute of Mathematics and Computer ScienceUniversity of LatviaRigaLatvia
  2. 2.Division of Computer ScienceHokkaido UniversitySapporoJapan
  3. 3.Division of Natural SciencesInternational Christian UniversityMitakaJapan

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