Complexity results for classes of quantificational formulas

Lewis, Harry R.

doi:10.1016/0022-0000(80)90027-6

Cited by 171 publications

(111 citation statements)

References 14 publications

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“…Kolaitis and Vardi [30] showed the satisfiability problem for Ackermann's class with equality is complete for NEXPTIME and that a 0-1 law holds for existential second-order logic 12 where the first-order part belongs to [∃ * ∀∃ * , all ] = . Lewis [33] proved that satisfiability for Ackermann's class without equality is complete for (deterministic) EXPTIME. Grädel [24] showed that satisfiability for Ackermann's class without equality is complete for EXPTIME even with the addition of arbitrarilymany function symbols.…”

Section: Ackermann's Class With Equalitymentioning

confidence: 99%

“…Ramsey [38] extended these results to the class with equality as part of a stronger result. Lewis [33] showed that satisfiability is NEXPTIME-complete for Ramsey's class and Kolaitis and Vardi [29] proved that a 0-1 law holds for existential second-order logic where the first-order part belongs to [∃ * ∀ * , all ] = . Omodeo and Policriti [36] have recently shown that the class is semidecidable for set theory.…”

Section: Ramsey's Classmentioning

confidence: 99%

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Testable and untestable classes of first-order formulae

Jordan

Zeugmann

2012

Journal of Computer and System Sciences

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In property testing, the goal is to distinguish structures that have some desired property from those that are far from having the property, based on only a small, random sample of the structure. We focus on the classification of first-order sentences according to their testability. This classification was initiated by Alon et al. [2], who showed that graph properties expressible with prefix ∃ * ∀ * are testable but that there is an untestable graph property expressible with quantifier prefix ∀ * ∃ * . The main results of the present paper are as follows. We prove that all (relational) properties expressible with quantifier prefix ∃ * ∀∃ * (Ackermann's class with equality) are testable and also extend the positive result of Alon et al.[2] to relational structures using a recent result by Austin and Tao [8]. Finally, we simplify the untestable property of Alon et al. [2] and show that prefixes ∀ 3 ∃, ∀ 2 ∃∀, ∀∃∀ 2 and ∀∃∀∃ can express untestable graph properties when equality is allowed.

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Section: Ackermann's Class With Equalitymentioning

confidence: 99%

Section: Ramsey's Classmentioning

confidence: 99%

Testable and untestable classes of first-order formulae

Jordan

Zeugmann

2012

Journal of Computer and System Sciences

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“…We adapt this proof to QFBAPA-Rel. The proof relies on the result [17] that acceptance of nondeterministic exponential-time bounded Turing machines can be reduced to satisfiability of formulas of the form ∃z.F 1 ∧ ∀y∃x.F 2 ∧ ∀y 1 ∀y 2 .F 3 where F 1 , F 2 , and F 3 have no quantifiers and are monadic (have only unary predicates). Given a formula of this from, we construct an equisatisfiable QFBAPA-Rel formula as a set of constraints, as follows.…”

Section: Complexity Of Qfbapa-relmentioning

confidence: 99%

“…The resulting QFBAPA-Rel formula is equisatisfiable with the original formula, so NEXPTIME lower bound follows from [17].…”

Section: Clauses Of the Formmentioning

confidence: 99%

Collections, Cardinalities, and Relations

Yessenov

Piskač

Kunčak

2010

Lecture Notes in Computer Science

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“…The problem is known to be EXPTIME-complete [17]. An example of the usefulness of multiple sorts in pure logic is Feferman's work [7] on interpolation theorems.…”

Section: Related Workmentioning

confidence: 99%

Toward a More Complete Alloy

Nelson

Dougherty

Fisler

et al. 2012

Abstract State Machines, Alloy, B, VDM, and Z

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Abstract. Many model-finding tools, such as Alloy, charge users with providing bounds on the sizes of models. It would be preferable to automatically compute sufficient upper-bounds whenever possible. The Bernays-Schönfinkel-Ramsey fragment of first-order logic can relieve users of this burden in some cases: its sentences are satisfiable iff they are satisfied in a finite model, whose size is computable from the input problem. Researchers have observed, however, that the class of sentences for which such a theorem holds is richer in a many-sorted framework-which Alloy inhabitsthan in the one-sorted case. This paper studies this phenomenon in the general setting of order-sorted logic supporting overloading and empty sorts. We establish a syntactic condition generalizing the Bernays-Schönfinkel-Ramsey form that ensures the Finite Model Property. We give a linear-time algorithm for deciding this condition and a polynomial-time algorithm for computing the bound on model sizes. As a consequence, model-finding is a complete decision procedure for sentences in this class. Our work has been incorporated into Margrave, a tool for policy analysis, and applies in real-world situations.

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Complexity results for classes of quantificational formulas

Cited by 171 publications

References 14 publications

Testable and untestable classes of first-order formulae

Testable and untestable classes of first-order formulae

Collections, Cardinalities, and Relations

Toward a More Complete Alloy

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