First-order spectra with one binary predicate

Durand, Arnaud; Ranaivoson, Solomampionona

doi:10.1007/bfb0022255

Computer Science Logic

1995

DOI: 10.1007/bfb0022255

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First-order spectra with one binary predicate

Arnaud Durand

Solomampionona Ranaivoson

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2004

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“…It is known from [27] that there is a first order sentence involving only one binary relation symbol the spectrum of which is NEXPTIME-complete, hence NPi-complete when the natural numbers are written in unary. It follows from [23] that this is also true if the vocabulary consists of two unary function symbols.…”

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confidence: 87%

On spectra of sentences of monadic second order logic with counting

Fischer

Makowsky

2004

J. symb. log.

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Abstract.We show that the spectrum of a sentence ϕ in Counting Monadic Second Order Logic (CMSOL) using one binary relation symbol and finitely many unary relation symbols, is ultimately periodic, provided all the models of ϕ are of clique width at most k, for some fixed k. We prove a similar statement for arbitrary finite relational vocabularies τ and a variant of clique width for τ-structures. This includes the cases where the models of ϕ are of tree width at most k. For the case of bounded tree-width, the ultimate periodicity is even proved for Guarded Second Order Logic GSOL. We also generalize this result to many-sorted spectra, which can be viewed as an analogue of Parikh's Theorem on context-free languages, and its analogues for context-free graph grammars due to Habel and Courcelle.Our work was inspired by Gurevich and Shelah (2003), who showed ultimate periodicity of the spectrum for sentences of Monadic Second Order Logic where only finitely many unary predicates and one unary function are allowed. This restriction implies that the models are all of tree width at most 2, and hence it follows from our result.

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confidence: 87%

On spectra of sentences of monadic second order logic with counting

Fischer

Makowsky

2004

J. symb. log.

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First-order spectra with one binary predicate

Cited by 1 publication

References 11 publications

On spectra of sentences of monadic second order logic with counting

On spectra of sentences of monadic second order logic with counting

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