Undecidable optimization problems for database logic programs

TL;DR: 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).

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