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Affine Systems of Equations and Counting Infinitary Logic

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Automata, Languages and Programming (ICALP 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4596))

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Abstract

We study the definability of constraint satisfaction problems (CSP) in various fixed-point and infinitary logics. We show that testing the solvability of systems of equations over a finite Abelian group, a tractable CSP that was previously known not to be definable in Datalog, is not definable in an infinitary logic with counting and hence that it is not definable in least fixed point logic or its extension with counting. We relate definability of CSPs to their classification obtained from tame congruence theory of the varieties generated by the algebra of polymorphisms of the template structure. In particular, we show that if this variety admits either the unary or affine type, the corresponding CSP is not definable in the infinitary logic with counting. We also study the complexity of determining whether a CSP omits unary and affine types.

Research supported by the Isaac Newton Institute, LAA programme.

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Authors and Affiliations

  1. Universitat Politécnica de Catalunya, Barcelona, Spain

    Albert Atserias

  2. Simon Fraser University, Burnaby BC, Canada

    Andrei Bulatov

  3. University of Cambridge Computer Laboratory, Cambridge, UK

    Anuj Dawar

Authors
  1. Albert Atserias
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  2. Andrei Bulatov
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  3. Anuj Dawar
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Lars Arge Christian Cachin Tomasz Jurdziński Andrzej Tarlecki

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Atserias, A., Bulatov, A., Dawar, A. (2007). Affine Systems of Equations and Counting Infinitary Logic . In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds) Automata, Languages and Programming. ICALP 2007. Lecture Notes in Computer Science, vol 4596. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73420-8_49

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  • DOI: https://doi.org/10.1007/978-3-540-73420-8_49

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73419-2

  • Online ISBN: 978-3-540-73420-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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