2026-08-10T20:05:08Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:1353 2024-03-06T10:32:59Z ddc:004 open_access

Order-Invariant MSO is Stronger than Counting MSO in the Finite Ganzow, Tobias Rubin, Sasha MSO Counting MSO order-invariance expressiveness Ehrenfeucht-Fraissé game We compare the expressiveness of two extensions of monadic second-order logic (MSO) over the class of finite structures. The first, counting monadic second-order logic (CMSO), extends MSO with first-order modulo-counting quantifiers, allowing the expression of queries like ``the number of elements in the structure is even''. The second extension allows the use of an additional binary predicate, not contained in the signature of the queried structure, that must be interpreted as an arbitrary linear order on its universe, obtaining order-invariant MSO. While it is straightforward that every CMSO formula can be translated into an equivalent order-invariant MSO formula, the converse had not yet been settled. Courcelle showed that for restricted classes of structures both order-invariant MSO and CMSO are equally expressive, but conjectured that, in general, order-invariant MSO is stronger than CMSO. We affirm this conjecture by presenting a class of structures that is order-invariantly definable in MSO but not definable in CMSO. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Tobias Ganzow and Sasha Rubin 2008 Is Part Of LIPIcs, Volume 1, 25th International Symposium on Theoretical Aspects of Computer Science (2008) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2008.1353 urn:nbn:de:0030-drops-13535 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1353 eng https://creativecommons.org/licenses/by-nd/3.0/legalcode