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Incomplete Transition Complexity of Some Basic Operations

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SOFSEM 2013: Theory and Practice of Computer Science (SOFSEM 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7741))

Abstract

Y. Gao et al. studied for the first time the transition complexity of Boolean operations on regular languages based on not necessarily complete DFAs. For the intersection and the complementation, tight bounds were presented, but for the union operation the upper and lower bounds differ by a factor of two. In this paper we continue this study by giving tight upper bounds for the concatenation, the Kleene star and the reversal operations. We also give a new tight upper bound for the transition complexity of the union, which refutes the conjecture presented by Y. Gao, et al.

This work was partially funded by the European Regional Development Fund through the programme COMPETE and by the Portuguese Government through the FCT under projects PEst-C/MAT/UI0144/2011 and CANTE-PTDC/EIA-CCO/101904/2008.

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Authors and Affiliations

  1. CMUP & DCC, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre, 4169-007, Porto, Portugal

    Eva Maia, Nelma Moreira & Rogério Reis

Authors
  1. Eva Maia
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  2. Nelma Moreira
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  3. Rogério Reis
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Science, University of Amsterdam, Plantage Muidergracht 24, 1018 TV, Amsterdam, The Netherlands

    Peter van Emde Boas

  2. Informatics Institute, Intelligent Systems Lab Amsterdam, University of Amsterdam, Science Park 904, 1098 XH, Amsterdam, The Netherlands

    Frans C. A. Groen

  3. Department of Civil Engineering and Computer Science, University of Rome Tor Vergata, Via del Politecnico 1, 00133, Rome, Italy

    Giuseppe F. Italiano

  4. Institute of Computing Science, Poznan University of Technology, ul. Piotrowo 2, 60-965, Poznan, Poland

    Jerzy Nawrocki

  5. Hasso-Plattner-Institute for Software Systems Engineering, Prof.-Dr.-Helmert-Str. 2-3, 14482, Potsdam, Germany

    Harald Sack

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Maia, E., Moreira, N., Reis, R. (2013). Incomplete Transition Complexity of Some Basic Operations. In: van Emde Boas, P., Groen, F.C.A., Italiano, G.F., Nawrocki, J., Sack, H. (eds) SOFSEM 2013: Theory and Practice of Computer Science. SOFSEM 2013. Lecture Notes in Computer Science, vol 7741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35843-2_28

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  • DOI: https://doi.org/10.1007/978-3-642-35843-2_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35842-5

  • Online ISBN: 978-3-642-35843-2

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