Showing papers by "Phokion G. Kolaitis published in 1990"
02 Apr 1990
TL;DR: It is shown here that the two dichotomies are indeed proper in terms of expressibility in Datalog(≠), and the expressibility of fixed subgraph homeomorphism queries on directed graphs is classified.
Abstract: We study here the language Datalog(≠), which is the query language obtained from Datalog by allowing equalities and inequalities in the bodies of the rules. We view Datalog(≠) as a fragment of an infinitary logic Lo and show that Lo can be characterized in terms of certain two-person pebble games. This characterization provides us with tools for investigating the expressive power of Datalog(≠). As a case study, we classify the expressibility of fixed subgraph homeomorphism queries on directed graphs. Fortune et al. [FHW80] classified the computational complexity of these queries by establishing two dichotomies, which are proper only if P ≠ NP. Without using any complexity-theoretic assumptions, we show here that the two dichotomies are indeed proper in terms of expressibility in Datalog(≠).
183 citations
04 Jun 1990
TL;DR: In this paper, the expressive power and computational strength of first-order implicit definability on finite structures are studied, and it is shown that every fixpoint query is a member of an implicitly definable pair of queries on finite structure.
Abstract: The expressive power and the computational strength of first-order implicit definability on finite structures are studied. It is shown that every fixpoint query is a member of an implicitly definable pair of queries on finite structures. This turns out to be an optimal result, since in addition it is proven that there are natural fixpoint queries that are not implicitly definable on finite structures. First-order implicit definability on ordered finite structures is also investigated, and logical characterization of the complexity class UP intersection coUP is obtained in terms of it, where UP is the class of NP languages accepted by unambiguous Turing machines. >
62 citations
TL;DR: It is established that a set of universal Horn clauses has a first-order circumscription if and only if it is bounded (when considered as a logic program); thus it is undecidable to tell whether such formulas have first- order circumscription.
Abstract: The effects of circumscribing first-order formulas are explored from a computational standpoint. First, extending work of V. Lifschitz, it is Shown that the circumscription of any existential first-order formula is equivalent to a first-order formula. After this, it is established that a set of universal Horn clauses has a first-order circumscription if and only if it is bounded (when considered as a logic program); thus it is undecidable to tell whether such formulas have first-order circumscription. Finally, it is shown that there arefirst-order formulas whode circumscription has a coNP-complete model-checking problem.
55 citations
01 Mar 1990
TL;DR: It is shown that zero-one law holds for the infinitary logic considered, i.e. the asymptotic probability of every sentence in this logic exists and is equal to either zero or one.
Abstract: Asymptotic probabilities of properties expressible in a certain infinitary logic on finite structures are investigated. Sentences in this logic may have arbitrary disjunctions and conjunctions, but they involve only a finite number of distinct variables. It is shown that zero-one law holds for the infinitary logic considered, i.e. the asymptotic probability of every sentence in this logic exists and is equal to either zero or one. This result subsumes earlier work on asymptotic probabilities for various fixpoint logics and reveals the boundary of zero-one laws for infinitary logics. >
39 citations
01 Dec 1990
TL;DR: In this paper, the authors investigated fragments of existential second-order logic in which the first-order part belongs to a prefix class and showed that the classifications of prefix classes with equality according to the solvability of the finite satisfiability problem are identical.
Abstract: The probability of a property on the collection of all finite relational structures is the limit as n --< infinity of the fraction of structures with n elements satisfying the property, provided the limit exists. It is known that the 0-1 law holds for any property expressible in first-order logic, i.e., the probability of any such property exists and is either 0 or 1. Moreover, the associated decision problem for the probabilities is solvable. We investigate here fragments of existential second-order logic in which we restrict the patterns of first-order quantifiers. We focus on fragments in which the first-order part belongs to a prefix class. We show that the classifications of prefix classes of first-order logic with equality according to the solvability of the finite satisfiability problem and according to the 0-1 law for the corresponding Sigma_1^1 fragment are identical.
14 citations
Proceedings Article•
01 Jan 1990
TL;DR: First-order implicit definability on ordered finite structures is investigated, and logical characterization of the complexity class UP intersection coUP is obtained in terms of it, where UP is the class of NP languages accepted by unambiguous Turing machines.
10 citations