Two variable logic with ultimately periodic counting

Conference item

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.

Authors: Benedikt, M; Kostylev, EV; Tan, T

• Alternative title: Conference paper
• Publication status: Published
• Peer review status: Reviewed (other)
• Publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
• Journal: Leibniz International Proceedings in Informatics
• Volume: 168
• Article number: 112
• Acceptance date: 2020-04-15
• Event title: 47th International Colloquium on Automata, Languages and Programming (ICALP 2020)
• Event location: Saarbrücken, Germany
• Event website: https://icalp2020.saarland-informatics-campus.de/
• Event start date: 2020-07-08
• Event end date: 2020-07-11
• DOI: 10.4230/LIPIcs.ICALP.2020.112
• ISSN: 1868-8969
• ISBN: 9783959771382
• Language: English
• Keywords: two-variable logic; Presburger arithmetic; FFR