Skip to main content
SpringerLink
Log in

Extending Finite Model Searching with Congruence Closure Computation

  • Conference paper
Artificial Intelligence and Symbolic Computation (AISC 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3249))

Abstract

The model generation problem, regarded as a special case of the Constraint Satisfaction Problem (CSP), has many applications in AI, computer science and mathematics. In this paper, we describe how to increase propagation of constraints by using the ground congruence closure algorithm. The experimental results show that using the congruence closure algorithm can reduce the search space for some benchmark problems.

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

Access this chapter

Log in via an institution
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Downey, P.J., Sethi, R., Tarjan, R.E.: Variations on the common subexpression problem. J. ACM 27(4), 758–771 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  2. Fujita, M., Slaney, J., Bennett, F.: Automatic generation of some results in finite algebra. In: Proc. 13th IJCAI, pp. 52–57 (1993)

    Google Scholar 

  3. Hasegawa, R., Koshimura, M., Fujita, H.: MGTP: A parallel theorem prover based on lazy model generation. In: Kapur, D. (ed.) CADE 1992. LNCS (LNAI), vol. 607, pp. 776–780. Springer, Heidelberg (1992)

    Google Scholar 

  4. Kim, S., Zhang, H.: ModGen: Theorem proving by model generation. In: Proc. 12th AAAI, pp. 162–167 (1994)

    Google Scholar 

  5. Kumar, V.: Algorithms for constraint satisfaction problems: A survey. AI Magazine 13(1), 32–44 (1992)

    Google Scholar 

  6. Manthey, R., Bry, F.: SATCHMO: A theorem prover implemented in Prolog. In: Lusk, E.‘., Overbeek, R. (eds.) CADE 1988. LNCS, vol. 310, pp. 415–434. Springer, Heidelberg (1988)

    Chapter  Google Scholar 

  7. McCune, W.: A Davis-Putnam program and its application to finite first-order model search: Quasigroup existence problems. Technical Report ANL/MCS-TM-194, Argonne National Laboratory (1994)

    Google Scholar 

  8. Nelson, G., Oppen, D.C.: Fast decision procedures based on congruence closure. J. ACM 27(2), 356–364 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  9. Nieuwenhuis, R., Oliveras, A.: Congruence closure with integer offsets. In: Y. Vardi, M., Voronkov, A. (eds.) LPAR 2003. LNCS (LNAI), vol. 2850, pp. 78–90. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  10. Slaney, J.: FINDER: Finite domain enumerator – system description. In: Bundy, A. (ed.) CADE 1994. LNCS, vol. 814, pp. 798–801. Springer, Heidelberg (1994)

    Google Scholar 

  11. Slaney, J., Fujita, M., Stickel, M.: Automated reasoning and exhaustive search: Quasigroup existence problems. Computers and Mathematics with Applications 29(2), 115–132 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  12. Sutcliffe, G., Suttner, C.: The TPTP problem library for automated theorem proving, http://www.cs.miami.edu/~tptp/

  13. Zhang, J.: Problems on the generation of finite models. In: Bundy, A. (ed.) CADE 1994. LNCS, vol. 814, pp. 753–757. Springer, Heidelberg (1994)

    Google Scholar 

  14. Zhang, J.: Constructing finite algebras with FALCON. J. Automated Reasoning 17(1), 1–22 (1996)

    Article  Google Scholar 

  15. Zhang, J., Zhang, H.: Constraint propagation in model generation. In: Montanari, U., Rossi, F. (eds.) CP 1995. LNCS, vol. 976, pp. 398–414. Springer, Heidelberg (1995)

    Google Scholar 

  16. Zhang, J., Zhang, H.: SEM: A system for enumerating models. In: Proc. 14th IJCAI, pp. 298–303 (1995)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, 100080, China

    Jian Zhang

  2. Department of Computer Science, University of Iowa, Iowa City, IA, 52242, USA

    Hantao Zhang

Authors
  1. Jian Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hantao Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria

    Bruno Buchberger

  2. Department of Computer Science, University College London, Gower Street, WC1E 6BT, London, UK

    John Campbell

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Zhang, J., Zhang, H. (2004). Extending Finite Model Searching with Congruence Closure Computation. In: Buchberger, B., Campbell, J. (eds) Artificial Intelligence and Symbolic Computation. AISC 2004. Lecture Notes in Computer Science(), vol 3249. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30210-0_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-30210-0_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23212-4

  • Online ISBN: 978-3-540-30210-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation