Non-Definability Results for Randomised First-Order Logic

Eickmeyer, Kord

doi:10.4230/LIPIcs.CSL.2011.218

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Non-Definability Results for Randomised First-Order Logic

Author Kord Eickmeyer

Part of: Volume: Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL (CSL 2011)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: Computer Science Logic (CSL)
License: Creative Commons Attribution-NoDerivs 3.0 Unported license
Publication Date: 2011-08-31

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DOI: 10.4230/LIPIcs.CSL.2011.218
URN: urn:nbn:de:0030-drops-32333

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Keywords

descriptive complexity
randomised logics
derandomisation

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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].

Cite As Get BibTex

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

Author Details

Kord Eickmeyer

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