Syntactic Complexity of Ideal and Closed Languages

  • Janusz Brzozowski
  • Yuli Ye
Conference paper

DOI: 10.1007/978-3-642-22321-1_11

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6795)
Cite this paper as:
Brzozowski J., Ye Y. (2011) Syntactic Complexity of Ideal and Closed Languages. In: Mauri G., Leporati A. (eds) Developments in Language Theory. DLT 2011. Lecture Notes in Computer Science, vol 6795. Springer, Berlin, Heidelberg

Abstract

The state complexity of a regular language is the number of states in the minimal deterministic automaton accepting the language. The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. The syntactic complexity of a subclass of regular languages is the worst-case syntactic complexity taken as a function of the state complexity n of languages in that class. We prove that nn − 1 is a tight upper bound on the complexity of right ideals and prefix-closed languages, and that there exist left ideals and suffix-closed languages of syntactic complexity nn − 1 + n − 1, and two-sided ideals and factor-closed languages of syntactic complexity nn − 2 + (n − 2)2n − 2 + 1.

Keywords

automaton closed complexity ideal language monoid regular reversal semigroup syntactic 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Janusz Brzozowski
    • 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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