A Decompositional Approach for Computing Least Fixed-Points of Datalog Programs with script Z sign-Counters

Constraints

Volumn 2, Issue 3-4, 1997, Pages 305-335

  Fribourg, Laurent ^a   Olsén, Hans ^b  

^a UNIVERSITÉ PARIS SACLAY   (France)

^b LINKÖPING UNIVERSITY   (Sweden)

Author keywords

Decomposition; Least fixed point; Linear arithmetic; Petri nets; Reachability set

Indexed keywords

EID: 0013423720     PISSN: 13837133     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1009747629591     Document Type: Article

References (38)

1. M. Ajmone Marsan, G. Balbo, G. Conte, S. Donatelli & G. Franceschinis. (1995). Modelling with Generalized Stochastic Petri Nets. John Wiley & Sons, Chichester.
2. M. Baudinet, M. Niezette & P. Wolper. (1991). On the Representation of Infinite Temporal Data Queries. Proc. 10th ACM Symp. on Principles of Database Systems, pages 280-290.
3. G. Berthelot. (1986). Transformations and Decompositions of Nets.Advances in Petri Nets, LNCS 254, pages 359-376, Springer-Verlag.
4. A. Boudet & H. Comon. (1996). Diophantine Equations, Presburger Arithmetic and Finite Automata. Proc. 21st Intl. Colloquium on Trees in Algebra and Programming, LNCS 1059, pages 30-43, Springer-Verlag.
5. G.W. Brams. (1983). Réseaux de Petri: Théorie et Pratique. Masson, Paris.
6. J. Chomicki & T. Imielinski. (1988). Temporal Deductive Databases and Infinite Objects. Proc. 7th ACM Symp. on Principles of Database Systems, Austin, pages 61-81.
7. S. Christensen. (1993). Decidability and Decompositionin Process Algebras. Ph.D. Thesis, University of Edinburgh, CST-105-93.
8. M. Clausen & A. Fortenbacher. (1989). Efficient Solution of Linear Diophantine Equations. J. Symbolic Computation 8:201-216.
9. P. Cousot & N. Halbwachs. (1978). Automatic Discovery of Linear Restraints among Variables of a Program. Conference Record 5th ACM Symp. on Principles of Programming Languages, Tucson, pages 84-96.
10. J. Esparza & M. Nielsen. (1994). Decidability Issues for Petri Nets. Bulletin of the EATCS, Number 52.
11. J. Esparza. (1995). Petri Nets, Commutative Context-Free Grammars, and Basic Parallel Processes. Proc. of Fundamentals of Computer Theory '95, LNCS 965, pages 221-232, Springer-Verlag.
12. L. Fribourg & M. Veloso Peixoto. (1994). Bottom-up Evaluation of Datalog Programs with Incremental Arguments and Linear Arithmetic Constraints. Proc. Post-ILPS'94 Workshop on Constraints and Databases, Ithaca, N.Y., pages 109-125.
13. L. Fribourg & H. Olsén. (1995). Datalog Programs with Arithmetical Constraints: Hierarchic, Periodic an Spiralling Least Fixpoints. Technical Report LIENS-95-26, Ecole Normale Supérieure, Paris.
14. L. Fribourg & H. Olsén. (1997). Proving Safety Properties of Infinite State Systems by Compilation into Presburger Arithmetic. Proc. 8th Intl. Conf. on Concurrency Theory, Warsaw, Poland, LNCS, Springer-Verlag.
15. A. Van Gelder. (1990). Deriving Constraints among Argument Sizes in Logic Programs. Proc. 9th ACM Symp. on Principles of Database Systems, Nashville, pages 47-60.
16. S. Ginsburg & E.H. Spanier. (1966). Semigroups, Presburger formulas and languages. Pacific Journal of Mathematics 16:285-296.
17. N. Halbwachs. (1993). Delay Analysis in Synchronous Programs. Proc. Computer Aided Verification, LNCS 697, pages 333-346, Springer-Verlag.
18. A.R. Helm. (1989). On the Detection and Elimination of Redundant Derivations during Bottom-up Execution. Proc. North American Conference on Logic Programming, Cleveland, Ohio, pages 945-961.
19. J. Hopcroft & J.-J. Pansiot. (1979). On the Reachability Problem for 5-dimensional Vector Addition Systems. Theoretical Computer Science8: 135-159.
20. J. Jaffar & J.L. Lassez. (1987). Constraint Logic Programming. Proc. 14th ACM Symp. on Principles of Programming Languages, pages 111-119.
21. F. Kabanza, J.M. Stevenne & P. Wolper. (1990). Handling Infinite Temporal Data. Proc. 9th ACM Symp. on Principles of Database Systems, Nashville, pages 392-403.
22. P. Kanellakis, G. Kuper & P. Revesz. (1990). Constraint Query Languages. Internal Report. (Short version in Proc. 9th ACM Symp. on Principles of Database Systems, Nashville, pages 299-313).
23. J.-L. Lassez & M.J. Maher. (1983). The Denotational Semantics of Horn Clauses As a Production System. Proc. AAAI-83, Washington D.C., pages 229-231.
24. D.W. Loveland. (1978). Automated Theorem Proving: A Logical Basis. North-Holland, Amsterdam.
25. M.J. Maher. (1988). Equivalences of Logic Programs. In J. Minker, editor, Foundations of Deductive Databases and of Logic Programming, pages 627-658. Morgan Kaufmann Publishers.
26. M.J. Maher. (1993). A Logic Programming View of CLP.Proc. 10th Intl. Conf. on Logic Programming, Budapest, pages 737-753.
27. S. Melzer & J. Esparza. (1995). Checking System Properties via Integer Programming. SFB-Bericht 342/13/95A, Technische Universitaet Muenchen. (See also: proceedings of ESOP '96).
28. J.F. Naughton & Y. Sagiv. (1987). A Decidable Class of Bounded Recursions. Proc. 6th ACM Symp. on Principles of Database Systems,San Diego, pages 171-180.
29. N.J. Nilsson. (1982). Principles of Artificial Intelligence. Springer-Verlag.
30. J.L. Peterson. (1981). Petri Net Theory and the Modeling of Systems. Prentice-Hall.
31. L. Plümer. (1990) Termination Proofs for Logic Programs based on Predicate Inequalities. Proc. 7th Intl. Conf. on Logic Programming, Jerusalem, pages 634-648.
32. R. Ramakrishnan, Y. Sagiv, J.D. Ulmann & M.Y. Vardi. (1989). Proof-Tree Transformation Theorems and their Applications. Proc. 8th ACM Symp. on Principles of Database Systems, Philadelphia, pages 172-181.
33. P. Revesz. (1990). A Closed Form for Datalog Queries with Integer Order. Proc. 3rd International Conference on Database Theory, Paris, pages 187-201.
34. D. Srivastava & R. Ramakrishnan. (1992). Pushing Constraints Selections. Proc. 11th ACM Symp. on Principles of Database Systems, San Diego, pages 301-315.
35. H. Tamaki & T. Sato. (1984). Unfold/fold Transformations of Logic Programs. Proc. 2nd Intl. Conf. on Logic Programming, Uppsala, pages 127-138.
36. K. Verschaetse & D. De Schreye. (1991). Deriving Termination Proofs for Logic Programs using Abstract Procedures. Proc. 8th Intl. Conf. on Logic Programming, Paris, pages 301-315.
37. L. Vieille. (1989). Recursive Query Processing: The Power of Logic. Theoretical Computer Science 69:1-53.
38. H.-C. Yen. (1996). On the Regularity of Petri Net Languages. Information and Computation 124:168-181.