Abstract
We investigate a class of set constraints defined as atomic set constraints augmented with projection. This class subsumes some already studied classes such as atomic set constraints with left-hand side projection and INES constraints. All these classes enjoy the nice property that satisfiability can be tested in cubic time. This is in contrast to several other classes of set constraints, such as definite set constraints and positive set constraints, for which satisfiability ranges from DEXPTIME-complete to NEXPTIME-complete. However, these latter classes allow set operators such as intersection or union which is not the case for the class studied here. In the case of atomic set constraints with projection one might expect that satisfiability remains polynomial. Unfortunately, we show that that the satisfiability problem for this class is no longer polynomial, but CoNP-hard. Furthermore, we devise a PSPACE algorithm to solve this satisfiability problem.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. Aiken. Set Constraints: Results, Applications, and Future Directions. In Proc. of the 2rd International Workshop on Principles and Practice of Constraint Programming, LNCS 874, pages 326–335. 1994.
A. Aiken. Introduction to Set Constraint-Based Program Analysis. In Science of Computer Programming, 35(2): 79–111, 1999.
A. Aiken, D. Kozen, M. Vardi and E. L. Wimmers. The complexity of set constraints. In 1993 Conference on Computer Science Logic, LNCS 832, pages 1–17, 1993.
A. Aiken, D. Kozen and E. Wimmers. Decidability of Systems of Set Constraints with Negative Constraints. Information and Computation, 122(1):30–44, oct 1995.
L. Bachmair, H. Ganzinger and U. Waldmann. Set constraints are the monadic class. In Proc. of the 8 th IEEE Symp. on Logic in Computer Science, pages 75–83, 1993.
W. Charatonik and L. Pacholski. Negative Set Constraints with Equality. In Proc. of the 9 th IEEE Symp. on Logic in Computer Science, pages 128–136, 1994.
W. Charatonik and L. Pacholski. Set Constraints with Projections are in NEXPTIME. In Proc. of the 35 th Symp. on Foundations of Computer Science, pages 642–653, 1994.
W Charatonik and A. Podelski. Set Constraints with Intersection. In Proc. of the 12 th IEEE Symp. on Logic in Computer Science, pages 362–372, 1997.
W. Charatonik and A. Podelski. Co-definite Set Constraints. In Proc. of the 9 th International Conference on Rewriting Techniques and Applications, LNCS 1379, pages 211–225, 1998.
W. Charatonik and J.-M. Talbot. Atomic Set Constraints with Projection. Research Report Max-Planck-Institut für Informatik. MPI-I-2002-2-008, 2002.
P. Devienne, J.-M. Talbot and S. Tison. Solving classes of set constraints with tree automata. In Proc. of the 3rd International Conference on Principles and Practice of Constraint Programming. LNCS 1330, pages 62–76, 1997.
R. Gilleron, S. Tison and M. Tommasi. Solving Systems of Set Constraints with Negated Subset Relationships. In Proc. of the 34th Symp. on Foundations of Computer Science, pages 372–380, 1993.
N. Heintze. Set Based Program Analysis. PhD thesis, Carnegie Mellon University, 1992.
N. Heintze and J. Jaffar. A Finite Presentation Theorem for Approximating Logic Programs. In Proc. of the 17 th Symp. on Principles of Programming Languages, pages 197–209, 1990.
N. Heintze and J. Jaffar. A Decision Procedure for a Class of Herbrand Set Constraints. In Proc. of the 5th IEEE Symp. on Logic in Computer Science, pages 42–51, 1990.
N. Heintze and J. Jaffar. Set constraints and set-based analysis. In Proc. of the Workshop on Principles and Practice of Constraint Programming, LNCS 874, pages 281–298, 1994.
F. Henglein and J. Rehof. The complexity of subtype entailment for simple types. In Proc. of the 12 th IEEE Symp. on Logic in Computer Science, pages 362–372, 1997.
J. Niehren, M. Müuller and J.-M. Talbot. Entailment of Atomic Set Constraints is PSPACE-Complete. In Proc. of the 14 th IEEE Symp. on Logic in Computer Science, pages 285–294, 1999.
M. Müuller, J. Niehren and A. Podelski. Inclusion Constraints over Non-Empty Sets of Trees. In Proc. of 7 th International Joint Conference CAAP/FASE-(TAPSOFT’97), LNCS 1214, pages 345–356, 1997.
L. Pacholski and A. Podelski. Set Constraints: A Pearl in Research on Constraints. In Proc. of the 3rd International Conference on Principles and Practice of Constraint Programming, LNCS 1330, pages 549–561, 1997. Tutorial.
J. C. Reynolds. Automatic computation of data set definitions. Information Processing, 68:456–461, 1969.
Savitch, W. Relationships between nondeterministic and deterministic tape complexities. Journal of Computer and System Sciences 4(2), 177–192.
K. Stefansson. Systems of Set Constraints with Negative Constraints are NEXPTIME-Complete. In Proc. of the 9 th IEEE Symp. on Logic in Computer Science, pages 137–141, 1994.
T. E. Uribe. Sorted Unification using Set Constraints. In Proc. of the 11th International Conference on Automated Deduction, LNAI 607, pages 163–177, 1992.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Charatonik, W., Talbot, JM. (2002). Atomic Set Constraints with Projection. In: Tison, S. (eds) Rewriting Techniques and Applications. RTA 2002. Lecture Notes in Computer Science, vol 2378. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45610-4_22
Download citation
DOI: https://doi.org/10.1007/3-540-45610-4_22
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43916-5
Online ISBN: 978-3-540-45610-0
eBook Packages: Springer Book Archive