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Monadic Second-Order Logics with Cardinalities

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Automata, Languages and Programming (ICALP 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2719))

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Abstract

We delimit the boundary between decidability versus undecidability of the weak monadic second-order logic of one successor (WS1S) extended with linear cardinality constraints of the form |X 1|+...+|X r| < |Y 1|+...+|Y s|, where the X is and Y js range over finite subsets of natural numbers. Our decidability and undecidability results are based on an extension of the classic logic-automata connection using a novel automaton model based on Parikh maps.

This work was supported by SRI International internal research and development, and NASA through contract NAS1-00079.

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Author information

Authors and Affiliations

  1. Albert-Ludwigs-Universität Freiburg, Germany

    Felix Klaedtke

  2. SRI International, CA, USA

    Harald Rueß

Authors
  1. Felix Klaedtke
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  2. Harald Rueß
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Editor information

Editors and Affiliations

  1. Dept. of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Jos C. M. Baeten

  2. School of Industrial and Systems Engineering, Georgia Institute of Technology, 765 Ferst Drive, Atlanta, GA, 30332-0205, USA

    Jan Karel Lenstra

  3. Department of Information Technology, Uppsala University, P.O. Box 337, 75105, Uppsala, Sweden

    Joachim Parrow

  4. Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    Gerhard J. Woeginger

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© 2003 Springer-Verlag Berlin Heidelberg

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Klaedtke, F., Rueß, H. (2003). Monadic Second-Order Logics with Cardinalities. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds) Automata, Languages and Programming. ICALP 2003. Lecture Notes in Computer Science, vol 2719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45061-0_54

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  • DOI: https://doi.org/10.1007/3-540-45061-0_54

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40493-4

  • Online ISBN: 978-3-540-45061-0

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