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. © 2008 Springer-Verlag Berlin Heidelberg.
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CITATION STYLE
Jordan, S., & Zeugmann, T. (2008). Indistinguishability and first-order logic. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4978 LNCS, pp. 94–104). Springer Verlag. https://doi.org/10.1007/978-3-540-79228-4_8
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