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Indistinguishability and First-Order Logic

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Theory and Applications of Models of Computation (TAMC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4978))

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Abstract

The “richness” of properties that are indistinguishable from first-order properties is investigated. Indistinguishability is a concept of equivalence among properties of combinatorial structures that is appropriate in the context of testability. All formulas in a restricted class of second-order logic are shown to be indistinguishable from first-order formulas. Arbitrarily hard properties, including RE-complete properties, that are indistinguishable from first-order formulas are shown to exist. Implications on the search for a logical characterization of the testable properties are discussed.

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Authors and Affiliations

  1. Division of Computer Science, Hokkaido University, N-14, W-9, Sapporo, 060-0814, Japan

    Skip Jordan & Thomas Zeugmann

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  1. Skip Jordan
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  2. Thomas Zeugmann
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Manindra Agrawal Dingzhu Du Zhenhua Duan Angsheng Li

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© 2008 Springer-Verlag Berlin Heidelberg

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Jordan, S., Zeugmann, T. (2008). Indistinguishability and First-Order Logic. In: Agrawal, M., Du, D., Duan, Z., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2008. Lecture Notes in Computer Science, vol 4978. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79228-4_8

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  • DOI: https://doi.org/10.1007/978-3-540-79228-4_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-79227-7

  • Online ISBN: 978-3-540-79228-4

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