Showing papers by "Moshe Y. Vardi published in 1987"

Undecidable Optimization Problems for Database Logic Programs

Abstract: Datalog is the language of logic programs without function symbols. It is used as a database query language. If it is possible to eliminate recursion from a Datalog program F’, then t’ is said to be bounded. It is shown that the problem of deciding whether a given Datalog program is bounded is undecidable, even for linear programs (i.e., programs in which each rule contains at most one occurrence of a recursive predicate). It is then shown that every semantic property of Datalog programs is undecidable if it is stable, is strongly nontrivial, and contains An earlier version of this work appeared under the same title in the Proceedings of the 2nd IEEE Symposium on Logic i~z Computer Science (Ithaca, N.Y.). IEEE, New York, 1987, pp. 106-115. Most of the research reported here was done while H. Gaifman was visiting the AI Center of SRI International whose support he wishes to acknowledge. He also wishes to thank IBM Watson Research Center and IBM Almaden Research Center for support in the summer of 1989, when the concluding work on this paper was done. The research reported here was done partly while H. Mairson was at the Computer Science Department of Stanford University and was supported by the Office of Naval Research (ONR) contract NOO014-85-C-0731 and partly while he was at the Programming Research Group of Oxford University. The research reported here was done while Y. Sagiv was visiting the Computer Science Department of Stanford University and was supported by a grant of AT & T Foundation, a grant of IBM Corporation and the National Science Foundation (NSF) grant 1ST 84-12791. Authors’ addresses: H. Gaifman and Y. Sagiv, Hebrew University, Jerusalem 91904, Israel; H. Mairson, Department of Computer Science, Brandeis University, Waltham, MA 02254; M. Y. Vardi, IBM Almaden Research Center, K53-802, 650 Harry Road, San Jose, CA 95120-6099. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage. the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission. 01993 ACM 0004-5411/93/0700-0683 $01.50 Journal of the Awxmt]on for Computing Machinery, VO1 40, No 3. July 1993. PP 683-713 684 H. GAIFMAN ET AL. boundedness. In particular, the property of being first-order 1s undecidable and (assuming that PTIME 1s different from LOGSPACE and from NC) the same holds for the property of being equivalent to a linear program and for the properties of being in LOGSPACE and of being in NC

The decision problem for the probabilities of higher-order properties

Abstract: The probability of a property on the class of all finite relational structures is the limit as n → ∞ of the fraction of structures with n elements satisfying the property, provided the limit exists. It is known that 0-1 laws hold for any property expressible in first-order logic or in fixpoint logic, i.e. the probability of any such property exists and is either 0 or 1. It is also known that the associated decision problem for the probabilities is PSPACE-complete and EXPTIME-complete for first-order logic and fixpoint logic respectively. The 0-1 law fails, however, in general for second-order properties and the decision problem becomes unsolvable. We investigate here logics which on the one hand go beyond fixpoint in terms of expressive power and on the other possess the 0-1 law. We consider first iterative logic which is obtained from first order logic by adding while looping as a construct. We show that the 0-1 law holds for this logic and determine the complexity of the associated decision problem. After this we study a fragment of second order logic called strict S11. This class of properties is obtained by restricting appropriately the first-order part of existential second-order sentences. Every strict S11 property is NP-computable and there are strict S11 properties that are NP-complete, such as 3-colorability. We show that the 0-1 law holds for strict S11 properties and establish that the associated decision problem is NEXPTIME-complete. The proofs of the decidability and complexity results require certain combinatorial machinery, namely generalizations of Ramsey's Theorem.

Verification of Concurrent Programs: The Automata-Theoretic Framework

Abstract: We present an automata-theoretic framework to the verification of concurrent and nondeterministic programs. The basic idea is that to verify that a program P is correct one writes a program A that receives the computation of P as input and diverges only on incorrect computations of P. Now P is correct if and only if a program P A , obtained by combining P and A, terminates. We formalize this idea in a framevork of ϖ-automata with a recursive set of states. This unifies previous works on verification of fair termination and verification of temporal properties

Unified Verification Theory

Abstract: We present an automata-theoretic framework to the verification of concurrent and nondeterministic programs. The basic idea is that to verify that a program P is correct one writes a program A that receives the computation of P as input and diverges only on incorrect computations of P. Now P is correct if and only if the program P A , which is obtained by combining P and A, terminates. This unifies previous works on verification of temporal properties and verification of fair termination.