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Non-Definability Results for Randomised First-Order Logic

Author Kord Eickmeyer



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LIPIcs.CSL.2011.218.pdf
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Kord Eickmeyer

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Kord Eickmeyer. Non-Definability Results for Randomised First-Order Logic. In Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 12, pp. 218-232, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2011)
https://doi.org/10.4230/LIPIcs.CSL.2011.218

Abstract

We investigate the expressive power of randomised first-order logic (BPFO) on restricted classes of structures. While BPFO is stronger than FO in general, even on structures with a built-in addition relation, we show that BPFO is not stronger than FO on structures with a unary vocabulary, nor on the class of equivalence relations. The same techniques can be applied to show that evenness of a linear order, and therefore graph connectivity, can not be defined in BPFO. Finally, we show that there is an FO[<]-definable query on word structures which can not be defined in BPFO[+1].
Keywords
  • descriptive complexity
  • randomised logics
  • derandomisation

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