Two Variable Logic with Ultimately Periodic Counting

Authors Michael Benedikt, Egor V. Kostylev, Tony Tan



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Author Details

Michael Benedikt
  • University of Oxford, UK
Egor V. Kostylev
  • University of Oxford, UK
Tony Tan
  • National Taiwan University, Taipei, Taiwan

Acknowledgements

We are grateful to Bartosz Bednarczyk for many useful comments and suggestions on preliminary drafts of this work.

Cite AsGet BibTex

Michael Benedikt, Egor V. Kostylev, and Tony Tan. Two Variable Logic with Ultimately Periodic Counting. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 112:1-112:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.ICALP.2020.112

Abstract

We consider the extension of FO² with quantifiers that state that the number of elements where a formula holds should belong to a given ultimately periodic set. We show that both satisfiability and finite satisfiability of the logic are decidable. We also show that the spectrum of any sentence is definable in Presburger arithmetic. In the process we present several refinements to the "biregular graph method". In this method, decidability issues concerning two-variable logics are reduced to questions about Presburger definability of integer vectors associated with partitioned graphs, where nodes in a partition satisfy certain constraints on their in- and out-degrees.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic
Keywords
  • Presburger Arithmetic
  • Two-variable logic

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