Skip to main content

A SAT-Based Decision Procedure for the Boolean Combination of Difference Constraints

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3542))

Abstract

The problem of deciding satisfiability of Boolean combinations of difference constraints is at the core of many important techniques such as planning, scheduling and bounded model checking of real-time systems. Efficient decision procedures for this class of formulas are, therefore, strongly needed. In this paper we present TSAT++, a system implementing a SAT-based decision procedure for this problem, and the techniques implemented in it; in particular, TSAT++ takes full advantage of recent SAT techniques. Comparative experimental results indicate that TSAT++ outperforms its competitors both on randomly generated, hand-made and real world problems.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Audemard, G., Bertoli, P.G., Cimatti, A., Kornilowicz, A., Sebastiani, R.: A SAT based approach for solving formulas over boolean and linear mathematical propositions. In: Voronkov, A. (ed.) CADE 2002. LNCS (LNAI), vol. 2392, pp. 195–210. Springer, Heidelberg (2002)

    Google Scholar 

  2. Armando, A., Castellini, C., Giunchiglia, E.: SAT-based procedures for temporal reasoning. In: Biundo, S., Fox, M. (eds.) ECP 1999. LNCS, vol. 1809, pp. 97–108. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  3. Armando, A., Castellini, C., Giunchiglia, E., Idini, M., Maratea, M.: TSAT++: an open platform for satisfiability modulo theories. In: Proceedings of PDPAR 2004 - Pragmatics of Decision Procedures in Automated Reasoning, Cork, Ireland. Elsevier Science Publishers, Amsterdam (2004) (to appear)

    Google Scholar 

  4. Bayardo Jr., R.J., Miranker, D.P.: A complexity analysis of space-bounded learning algorithms for the constraint satisfaction problem. In: Proc. AAAI, pp. 298–304 (1996)

    Google Scholar 

  5. Bayardo Jr., R.J., Schrag, R.C.: Using CSP look-back techniques to solve real-world SAT instances. In: Proceedings of the 14th National Conference on Artificial Intelligence and 9th Innovative Applications of Artificial Intelligence Conference (AAAI 1997/IAAI 1997), July 27–31, pp. 203–208. AAAI Press, Menlo Park (1997)

    Google Scholar 

  6. Le Berre, D., Simon, L.: The essentials of the SAT 2003 competition. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 452–467. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  7. Cormen, T.H., Leiserson, C.E., Rivest, R.R.: Introduction to Algorithms. MIT Press, Cambridge (1998)

    Google Scholar 

  8. CPLEX user’s guide. Manual, CPLEX Optimization, Inc., Incline Village, NV, USA (1993)

    Google Scholar 

  9. Dechter, R., Meiri, I., Pearl, J.: Temporal constraint networks. Artificial Intelligence 49(1-3), 61–95 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  10. Gerevini, A., Cristani, M.: On finding a solution in temporal constraint satisfaction problems. In: Proceedings of the 15th International Joint Conference on Artificial Intelligence (IJCAI 1997), August 23–29, pp. 1460–1465. Morgan Kaufmann Publishers, San Francisco (1997)

    Google Scholar 

  11. Giunchiglia, E., Maratea, M., Tacchella, A.: Look-ahead vs. look-back techniques in a modern SAT solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  12. Li, C.M., Anbulagan: Heuristics based on unit propagation for satisfiability problems. In: Proceedings of the 15th International Joint Conference on Artificial Intelligence (IJCAI 1997), August 23–29, pp. 366–371. Morgan Kaufmann Publishers, San Francisco (1997)

    Google Scholar 

  13. Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an Efficient SAT Solver. In: Proceedings of the 38th Design Automation Conference, DAC 2001 (June 2001)

    Google Scholar 

  14. Oddi, A., Cesta, A.: Incremental forward checking for the disjunctive temporal problem. In: Proceedings of the 14th European Conference on Artificial Intelligence (ECAI 2000), Berlin, pp. 108–112 (2000)

    Google Scholar 

  15. Prosser, P.: Hybrid algorithms for the constraint satisfaction problem. Computational Intelligence 9(3), 268–299 (1993)

    Article  Google Scholar 

  16. Stergiou, K., Koubarakis, M.: Backtracking algorithms for disjunctions of temporal constraints. In: Proc. AAAI (1998)

    Google Scholar 

  17. Silva, J.P.M., Sakallah, K.A.: GRASP: A search algorithm for propositional satisfiability. IEEETC: IEEE Transactions on Computers 48 (1999)

    Google Scholar 

  18. Strichman, O., Seshia, S.A., Bryant, R.E.: Deciding separation formulas with SAT. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 209–222. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  19. Tsamardinos, I., Pollack, M.: Efficient solution techniques for disjunctive temporal reasoning problems. Artificial Intelligence (2003) (to appear)

    Google Scholar 

  20. Wolfman, S., Weld, D.: The LPSAT-engine & its application to resource planning. In: Proc. IJCAI 1999 (1999)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Armando, A., Castellini, C., Giunchiglia, E., Maratea, M. (2005). A SAT-Based Decision Procedure for the Boolean Combination of Difference Constraints. In: Hoos, H.H., Mitchell, D.G. (eds) Theory and Applications of Satisfiability Testing. SAT 2004. Lecture Notes in Computer Science, vol 3542. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11527695_2

Download citation

  • DOI: https://doi.org/10.1007/11527695_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-27829-0

  • Online ISBN: 978-3-540-31580-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics