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Tatsuya Gima

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Preprint Aug 2026

Extending Courcelle's Theorem with Optimality Predicates

A new logic is introduced, which extends $\mathsf{CMSO}$ with predicates for membership in the families of minimum- and maximum-cardinality sets satisfying a fixed formula $\phi(X)$, and algorithmic meta-theorems based on fixed-parameter tractable model checking are given.

Tatsuya Gima · 0 citations
Preprint Aug 2026

Quantifying over Optimal MSO-Definable Sets on Graphs of Bounded Clique-Width

We introduce $\mathsf{AmCMSO}$, an extension of counting monadic second-order logic ($\mathsf{CMSO}$) with predicates that refer to minimum- and maximum-value satisfying assignments. We establish fixed-parameter tractable model-checking meta-theorems for $\mathsf{AmCMSO}_1$ on graphs of bounded clique-width and for $\m...

Tatsuya Gima · 0 citations

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