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On the Complexity of Symbolic Verification and Decision Problems in Bit-Vector Logic

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Mathematical Foundations of Computer Science 2014 (MFCS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8635))

Abstract

We study the complexity of decision problems encoded in bit-vector logic. This class of problems includes word-level model checking, i.e., the reachability problem for transition systems encoded by bit-vector formulas. Our main result is a generic theorem which determines the complexity of a bit-vector encoded problem from the complexity of the problem in explicit encoding. In particular, NL-completeness of graph reachability directly implies PSpace-completeness and ExpSpace-completeness for word-level model checking with unary and binary arity encoding, respectively. In general, problems complete for a complexity class C are shown to be complete for an exponentially harder complexity class than C when represented by bit-vector formulas with unary encoded scalars, and further complete for a double exponentially harder complexity class than C with binary encoded scalars. We also show that multi-logarithmic succinct encodings of the scalars result in completeness for multi-exponentially harder complexity classes. Technically, our results are based on concepts from descriptive complexity theory and related techniques for OBDDs and Boolean encodings.

Supported by the NFN grant S11403-N23 (RiSE) of the Austrian Science Fund (FWF) and by the grant ICT10-050 (PROSEED) of the Vienna Science and Technology Fund (WWTF).

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Authors and Affiliations

  1. Formal Methods in Systems Engineering Group, Vienna University of Technology, Wien, Austria

    Gergely Kovásznai & Helmut Veith

  2. Institute for Formal Models and Verification, Johannes Kepler University, Linz, Austria

    Andreas Fröhlich & Armin Biere

Authors
  1. Gergely Kovásznai
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  2. Helmut Veith
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  3. Andreas Fröhlich
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  4. Armin Biere
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Editor information

Editors and Affiliations

  1. Faculty of Informatics, Eötvös Loránd University, Pázmány Péter sétány 1/C, 1117, Budapest, Hungary

    Erzsébet Csuhaj-Varjú

  2. Fakultät für Informatik und Automatisierung, Technische Universität Ilmenau, Helmholtzplatz, 598693, Ilmenau, Germany

    Martin Dietzfelbinger

  3. Institute of Informatics, Szeged University, Tisza Lajos krt. 103, 6720, Szeged, Hungary

    Zoltán Ésik

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Kovásznai, G., Veith, H., Fröhlich, A., Biere, A. (2014). On the Complexity of Symbolic Verification and Decision Problems in Bit-Vector Logic. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds) Mathematical Foundations of Computer Science 2014. MFCS 2014. Lecture Notes in Computer Science, vol 8635. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44465-8_41

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  • DOI: https://doi.org/10.1007/978-3-662-44465-8_41

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44464-1

  • Online ISBN: 978-3-662-44465-8

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