Capturing complexity classes by fragments of second-order logic
Theoretical Computer Science - Special issue on logic and applications to computer science
Finite-model theory—a personal perspective
ICDT Selected papers of the 4th international conference on Database theory
Monadic logical definability of nondeterministic linear time
Computational Complexity
A Conjunctive Logical Characterization of Nondeterministic Linear Time
CSL '97 Selected Papers from the11th International Workshop on Computer Science Logic
Existential second-order logic over graphs: Charting the tractability frontier
Journal of the ACM (JACM)
Graph properties checkable in linear time in the number of vertices
Journal of Computer and System Sciences
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On Definability in Dependence Logic
Journal of Logic, Language and Information
A hierarchy for nondeterministic time complexity
Journal of Computer and System Sciences
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We study fragments D(k∀) and D(k-dep) of dependence logic defined either by restricting the number k of universal quantifiers or the width of dependence atoms in formulas. We find the sublogics of existential second-order logic corresponding to these fragments of dependence logic. We also show that, for any fixed signature, the fragments D(k∀) give rise to an infinite hierarchy with respect to expressive power. On the other hand, for the fragments D(k-dep), a hierarchy theorem is otained only in the case the signature is also allowed to vary. For any fixed signature, this question is open and is related to the so-called Spectrum Arity Hierarchy Conjecture.