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Graph Structure and Monadic Second-Order Logic by Joost Engelfriet, Bruno Courcelle

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Hopefully tractable monadic second-order properties

Our aim is here to identify classes of monadic second-order graph properties for which the associated automata have manageable sizes. These properties are expressible without quantifier alternation in terms of some “basic” monadic second-order properties.

Definition 6.41 Let image be a set of pairwise inequivalent formulas in CMS′(s,ω) such that the set of free variables of any φ ∈ is mfv(φ). The integer ...

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