Degrees of acyclicity for hypergraphs and relational database schemes
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Syntax vs. Semantics on Finite Structures
Structures in Logic and Computer Science, A Selection of Essays in Honor of Andrzej Ehrenfeucht
Will Deflation Lead to Depletion? On Non-Monotone Fixed Point Inductions
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
Existential second-order logic over graphs: Charting the tractability frontier
Journal of the ACM (JACM)
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
Graphs, Networks and Algorithms
Graphs, Networks and Algorithms
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We study properties characterized by applying successively a "destructive" rule expressed in first-order logic. The rule says that points a 1, ..., a k of a structure can be removed if they satisfy a certain first-order formula φ(a 1, ...,a k ). The property defined this way by the formula is the set of finite structures such that we are able to obtain the empty structure when applying the rule repeatedly. Many classical properties can be formulated by means of a "destructive" rule. We do a systematic study of the computational complexity of these properties according to the fragment of first-order logic in which the rule is expressed. We give the list of minimal fragments able to define NP-complete properties and maximal fragments that define only PTIME properties (unless PTIME = NP), depending on the number k of free variables and the quantifier symbols used in the formula. We also study more specifically the case where the formula has one free variable and is universal.