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In the particular cases where the operations are defined by quantifier-free (QF) formulas, the quantifier-heights of the obtained sentences are no larger than those of the input ones. It follows that the class of finite models of a FO sentence is recognizable with respect to the considered QF operations. Recognizability has interesting algorithmic properties based on finite automata on terms, for structures having bounded tree-width or clique-width.
We extend our results to FO sentences constructed with modulo counting existential quantifiers.
From: Bruno Courcelle [view email]
[v1]
Fri, 29 May 2026 12:55:03 UTC (156 KB)
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