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International Colloquium on Automata, Languages, and Programming

ICALP 2008: Automata, Languages and Programming pp 63–74Cite as

On the Computational Completeness of Equations over Sets of Natural Numbers

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5126))

Abstract

Systems of equations of the form ϕ j (X 1, ..., X n ) = ψ j (X 1, ..., X n ) with \(1 \leqslant j \leqslant m\) are considered, in which the unknowns X i are sets of natural numbers, while the expressions ϕ j ,ψ j may contain singleton constants and the operations of union (possibly replaced by intersection) and pairwise addition . It is shown that the family of sets representable by unique (least, greatest) solutions of such systems is exactly the family of recursive (r.e., co-r.e., respectively) sets of numbers. Basic decision problems for these systems are located in the arithmetical hierarchy.

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Author information

Authors and Affiliations

  1. Institute of Computer Science, University of Wrocław, Poland

    Artur Jeż

  2. Academy of Finland,  

    Alexander Okhotin

  3. Department of Mathematics, University of Turku, Finland

    Alexander Okhotin

Authors
  1. Artur Jeż
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  2. Alexander Okhotin
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Editor information

Luca Aceto Ivan Damgård Leslie Ann Goldberg Magnús M. Halldórsson Anna Ingólfsdóttir Igor Walukiewicz

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Jeż, A., Okhotin, A. (2008). On the Computational Completeness of Equations over Sets of Natural Numbers. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds) Automata, Languages and Programming. ICALP 2008. Lecture Notes in Computer Science, vol 5126. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70583-3_6

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  • DOI: https://doi.org/10.1007/978-3-540-70583-3_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-70582-6

  • Online ISBN: 978-3-540-70583-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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