@inproceedings{07a3e94d4fa44aa18c64b176e6070d87,
title = "From Sets to Points: Simplifying MSO Interpretations via Reparameterizations",
abstract = "We study the conditions under which monadic second-order (MSO) interpretations can be simplified by replacing representations of elements as tuples of arbitrary sets with representations as tuples of finite sets or points. Using reparameterizations of MSO formulas, we prove that for formulas with free finite-set variables, it is decidable whether a point reparameterization exists, and that such a reparameterization can be effectively constructed over countable chains. Moreover, over countable Dedekind-complete labeled chains, a formula with free arbitrary set variables admits a finite-set reparameterization if and only if it has at most countably many satisfying assignments. These results yield effective simplification procedures for MSO interpretations over broad classes of countable linear orders.",
keywords = "MSO interpretation, Monadic Second-Order Logic, decidability, interpretation simplification, reparameterization",
author = "Alexander Rabinovich",
note = "Publisher Copyright: {\textcopyright} Alexander Rabinovich.; 53rd International Colloquium on Automata, Languages, and Programming, ICALP 2026 ; Conference date: 07-07-2026 Through 10-07-2026",
year = "2026",
month = jul,
day = "1",
doi = "10.4230/LIPIcs.ICALP.2026.189",
language = "English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Sayan Bhattacharya and Danupon Nanongkai and Michael Benedikt and Gabriele Puppis",
booktitle = "53rd International Colloquium on Automata, Languages, and Programming, ICALP 2026",
address = "Germany",
}