Syntactic Complexity of Prefix-, Suffix-, and Bifix-Free Regular Languages

  • Janusz Brzozowski
  • Baiyu Li
  • Yuli Ye
Conference paper

DOI: 10.1007/978-3-642-22600-7_8

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6808)
Cite this paper as:
Brzozowski J., Li B., Ye Y. (2011) Syntactic Complexity of Prefix-, Suffix-, and Bifix-Free Regular Languages. In: Holzer M., Kutrib M., Pighizzini G. (eds) Descriptional Complexity of Formal Systems. DCFS 2011. Lecture Notes in Computer Science, vol 6808. Springer, Berlin, Heidelberg

Abstract

The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. The syntactic complexity of a subclass of the class of regular languages is the maximal syntactic complexity of languages in that class, taken as a function of the state complexity n of these languages. We study the syntactic complexity of prefix-, suffix-, and bifix-free regular languages. We prove that nn − 2 is a tight upper bound for prefix-free regular languages. We present properties of the syntactic semigroups of suffix- and bifix-free regular languages, and conjecture tight upper bounds on their size.

Keywords

bifix-free finite automaton monoid prefix-free regular language semigroup suffix-free syntactic complexity 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Janusz Brzozowski
    • 1
  • Baiyu Li
    • 1
  • Yuli Ye
    • 2
  1. 1.David R. Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada
  2. 2.Department of Computer ScienceUniversity of TorontoTorontoCanada

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