@inproceedings{DBLP:conf/pods/MumickS94, author = {Inderpal Singh Mumick and Oded Shmueli}, title = {Universal Finiteness and Satisfiability}, booktitle = {Proceedings of the Thirteenth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, May 24-26, 1994, Minneapolis, Minnesota}, publisher = {ACM Press}, year = {1994}, isbn = {0-89791-642-5}, pages = {190-200}, ee = {http://doi.acm.org/10.1145/182591.182612, db/conf/pods/pods94-190.html}, crossref = {DBLP:conf/pods/94}, bibsource = {DBLP, http://dblp.uni-trier.de} }

The problem of determining whether, for every extensional database, a given predicate in a given program has a finite number of derivations is called the universal finiteness problem. The problem of determining whether a given predicate in a given program has a non-empty extension for some extensional database is called the satisfiability problem. We show that the universal finiteness problem can be reduced to the satisfiability problem. Thus all decidability results for satisfiability can be applied to universal finiteness - for example, we can infer that the universal finiteness problem is decidable for Datalog extended with negation on base predicates. The satisfiability problem can be easily reduced to the universal finiteness problem, so that all undecidability results for satisfiability can be applied to universal finiteness. For example we can infer that the universal finiteness problem is undecidable for Datalog extended with stratified negation.

Many recursive programs have infinite number of derivations only when
edb relations have data cycles. It is thus of particular interest to
study universal finiteness in the presence of acyclicity constraints
on the edb relations. We define acyclicity constraints in terms of
non-satisfiability of a specific recursive program. We show that both
the problems of universal finiteness and satisfiability of Datalog in
the presence of acyclicity constraints (on one or more edb relations)
remain decidable for a language *L* whenever the problems are
decidable for language *L* in absence of such constraints. We also
show that the problems are undecidable for arbitrary constraints
expressed in terms of non-satisfiability of a recursive program.

*Copyright © 1994 by the ACM,
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Contents

[Full Text in PDF Format, 1111 KB]

- [Abi89]
- Serge Abiteboul: Boundedness is Undecidable for Datalog Programs with a Single Recursive Rule. Inf. Process. Lett. 32(6): 281-287(1989)
- [CGKV88]
- Stavros S. Cosmadakis, Haim Gaifman, Paris C. Kanellakis, Moshe Y. Vardi: Decidable Optimization Problems for Database Logic Programs (Preliminary Report). STOC 1988: 477-490
- [GKM92]
- Ashish Gupta, Dinesh Katiyar, Inderpal Singh Mumick: Counting solutions to the View Maintenance Problem. Workshop on Deductive Databases, JICSLP 1992: 185-194
- [GMSV87]
- Haim Gaifman, Harry G. Mairson, Yehoshua Sagiv, Moshe Y. Vardi: Undecidable Optimization Problems for Database Logic Programs. LICS 1987: 106-115
- [GMS93]
- Ashish Gupta, Inderpal Singh Mumick, V. S. Subrahmanian: Maintaining Views Incrementally. SIGMOD Conference 1993: 157-166
- [Gue90]
- Irène Guessarian: Deciding Boundedness for Uniformly Connected Datalog Programs. ICDT 1990: 395-405
- [HKMV91]
- Gerd G. Hillebrand, Paris C. Kanellakis, Harry G. Mairson, Moshe Y. Vardi: Tools for Datalog Boundedness. PODS 1991: 1-12
- [ISO93]
- ...
- [KKR90]
- Paris C. Kanellakis, Gabriel M. Kuper, Peter Z. Revesz: Constraint Query Languages. PODS 1990: 299-313
- [LMSS93]
- Alon Y. Levy, Inderpal Singh Mumick, Yehoshua Sagiv, Oded Shmueli: Equivalence, Query-Reachability, and Satisfiability in Datalog Extensions. PODS 1993: 109-122
- [LS92]
- Alon Y. Levy, Yehoshua Sagiv: Constraints and Redundancy in Datalog. PODS 1992: 67-80
- [MFPR90]
- Inderpal Singh Mumick, Sheldon J. Finkelstein, Hamid Pirahesh, Raghu Ramakrishnan: Magic is Relevant. SIGMOD Conference 1990: 247-258
- [MPR90]
- Inderpal Singh Mumick, Hamid Pirahesh, Raghu Ramakrishnan: The Magic of Duplicates and Aggregates. VLDB 1990: 264-277
- [MR89]
- Michael J. Maher, Raghu Ramakrishnan: Déjà Vu in Fixpoints of Logic Programs. NACLP 1989: 963-980
- [MS93]
- Inderpal Singh Mumick, Oded Shmueli: Finiteness Properties of Database Queries. Australian Database Conference 1993: 274-288
- [Mum91]
- ...
- [Nau86]
- Jeffrey F. Naughton: Data Independent Recursion in Deductive Databases. J. Comput. Syst. Sci. 38(2): 259-289(1989)
- [NS87]
- Jeffrey F. Naughton, Yehoshua Sagiv: A Decidable Class of Bounded Recursions. PODS 1987: 227-236
- [Shm87]
- Oded Shmueli: Decidability and Expressiveness of Logic Queries. PODS 1987: 237-249
- [SS86]
- ...
- [UVG88]
- Jeffrey D. Ullman, Allen Van Gelder: Parallel Complexity of Logical Query Programs. Algorithmica 3: 5-42(1988)
- [vdM90]
- ...
- [vdM92]
- ...
- [Var88]
- Moshe Y. Vardi: Decidability and Undecidability Results for Boundedness of Linear Recursive Queries. PODS 1988: 341-351