Work

Generalised Quantifiers Based on Rabin-Mostowski Index

Year: 2026

Type: preprint

Abstract: In this work we introduce new generalised quantifiers which allow us to express the Rabin-Mostowski index of automata. Our main results study expressive power and decidability of the monadic second-order (MSO) logic extended with these quantifiers. We study these problems in the realm of both $ω$-words and infinite trees. As it turns out, the pictures in these two cases are very different. In the case of $ω$-words the new quantifiers can be effectively expressed in pure MSO logic. In contrast, in the case of infinite trees, addition of these quantifiers leads to an undecidable formalism. To realise index-quantifier elimination, we consider the extension of MSO by game quantifiers. As a tool, we provide a specific quantifier-elimination procedure for them. Moreover, we introduce a novel construction of transducers realising strategies in $ω$-regular games with monadic parameters.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2601.04739

Authors: Kuperberg, Denis, Niwiński, Damian, Parys, Paweł, Skrzypczak, Michał

Institutions: École Normale Supérieure de Lyon, Centre National de la Recherche Scientifique, Laboratoire de l'Informatique du Parallélisme, University of Warsaw

Topic: semigroups and automata theory

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7119789981

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