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Syntactic Complexity of Ideal and Closed Languages

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Developments in Language Theory (DLT 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6795))

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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 n n − 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 n n − 1 + n − 1, and two-sided ideals and factor-closed languages of syntactic complexity n n − 2 + (n − 2)2n − 2 + 1.

This work was supported by the Natural Sciences and Engineering Research Council of Canada under grant No. OGP0000871 and a Postgraduate Scholarship, and by a Graduate Award from the Department of Computer Science, University of Toronto.

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Authors and Affiliations

  1. David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, Canada, N2L 3G1

    Janusz Brzozowski

  2. Department of Computer Science, University of Toronto, Toronto, ON, Canada, M5S 3G4

    Yuli Ye

Authors
  1. Janusz Brzozowski
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  2. Yuli Ye
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  1. Dipartimento di Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano-Bicocca, Viale Sarca 336, Edificio U14, 20126, Milano, Italy

    Giancarlo Mauri  & Alberto Leporati  & 

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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. https://doi.org/10.1007/978-3-642-22321-1_11

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  • DOI: https://doi.org/10.1007/978-3-642-22321-1_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22320-4

  • Online ISBN: 978-3-642-22321-1

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