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IFIP International Conference on Theoretical Computer Science

TCS 2012: Theoretical Computer Science pp 164–178Cite as

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On Properties and State Complexity of Deterministic State-Partition Automata

On Properties and State Complexity of Deterministic State-Partition Automata

  • Galina Jirásková18 &
  • Tomáš Masopust19 
  • Conference paper
  • 871 Accesses

  • 8 Citations

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7604)

Abstract

A deterministic automaton accepting a regular language L is a state-partition automaton with respect to a projection P if the state set of the deterministic automaton accepting the projected language P(L), obtained by the standard subset construction, forms a partition of the state set of the automaton. In this paper, we study fundamental properties of state-partition automata. We provide a construction of the minimal state-partition automaton for a regular language and a projection, discuss closure properties of state-partition automata under the standard constructions of deterministic automata for regular operations, and show that almost all of them fail to preserve the property of being a state-partition automaton. Finally, we define the notion of a state-partition complexity, and prove the tight bound on the state-partition complexity of regular languages represented by incomplete deterministic automata.

Keywords

  • Regular languages
  • finite automata
  • descriptional complexity
  • projections
  • state-partition automata

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References

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Author information

Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, 040 01, Košice, Slovak Republic

    Galina Jirásková

  2. Institute of Mathematics, Academy of Sciences of the Czech Republic, Žižkova 22, 616 62, Brno, Czech Republic

    Tomáš Masopust

Authors
  1. Galina Jirásková
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  2. Tomáš Masopust
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Editor information

Editors and Affiliations

  1. Centrum Wiskunde & Informatica (CWI), Science Park 123, 1098 XG, Amsterdam, The Netherlands

    Jos C. M. Baeten & Frank S. de Boer & 

  2. Microsoft Research, One Microsoft Way, 98052, Redmond, WA, USA

    Tom Ball

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© 2012 IFIP International Federation for Information Processing

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Jirásková, G., Masopust, T. (2012). On Properties and State Complexity of Deterministic State-Partition Automata. In: Baeten, J.C.M., Ball, T., de Boer, F.S. (eds) Theoretical Computer Science. TCS 2012. Lecture Notes in Computer Science, vol 7604. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33475-7_12

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  • DOI: https://doi.org/10.1007/978-3-642-33475-7_12

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  • Print ISBN: 978-3-642-33474-0

  • Online ISBN: 978-3-642-33475-7

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