Computing prime implicates incrementally

  • Peter Jackson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 607)


We describe an algorithm (called PIGLET) which takes a theory already in prime implicate form and computes the prime implicates of that theory extended by a single clause. Then we compare PIGLET's performance with that of an alternative algorithm for this incremental computation (called IPIA). We critique some optimizations that have been proposed for IPIA, and show that two of them interact to render the modified method incomplete. Finally, we present data which show that PIGLET outperforms IPIA, in that it generates a smaller search space and takes less CPU time. Its superiority is evident both when updating a randomly-generated theory by a random clause and when we generalize the two programs for the task of updating by more than one clause. Its high performance is mainly due to heuristics which capitalize on merges to promote early backward subsumption and pre-empt forward subsumption.


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  1. 1.
    R. H. Brayton, G. D. Hachtel, C. T. McMullen, A. L. Sangiovanni-Vincentelli: Logic Minimization Algorithms for VLSI Synthesis. Boston, MA: Kluwer-Academic, 1984.Google Scholar
  2. 2.
    T. Dean, M. Boddy: An analysis of time-dependent planning. 7th AAAI, 49–54, 1988.Google Scholar
  3. 3.
    E. Eder: Consolution and its relation with resolution. 12th IJCAI, 132–136, 1991.Google Scholar
  4. 4.
    P. Jackson: The SLOOP Manual. Artificial Intelligence Applications Institute, Edinburgh University, 1987.Google Scholar
  5. 5.
    P. Jackson: Computing prime implicates. Proceedings 20th Annual Computer Science Conference, 65–72, New York: ACM Press, 1992.Google Scholar
  6. 6.
    P. Jackson: Computing minimal refutations. Proceedings of 3rd Scandinavian Conference on Artificial Intelligence, 107–118, Amsterdam: IOS Press, 1991.Google Scholar
  7. 7.
    P. Jackson: Possibilistic prime implicates and their use in abduction. Proceedings of AAAI-91 Workshop on Abduction, 44–50, 1991.Google Scholar
  8. 8.
    P. Jackson, J. Pais: Computing prime implicants. Proceedings of 10th International Conference on Automated Deduction, 543–557, 1990.Google Scholar
  9. 9.
    A. Kean, Tsiknis, G: An incremental method for generating prime implicants/ implicates. J. Symb. Comp., 9, 185–206, 1990.Google Scholar
  10. 10.
    E. L. McCluskey Jr: Minimization of Boolean functions. Bell Systems Technical Journal, 35, 1417–1444, 1956.Google Scholar
  11. 11.
    S. Muroga: Logic Design and Switching Theory. New York, NY: Wiley, 1979.Google Scholar
  12. 12.
    J. Pais, P. Jackson: Partial monotonicity and a new version of the Ramsey Test To appear in Studia Logica.Google Scholar
  13. 13.
    W. V. O. Quine: The problem of simplifying truth functions. American Mathematical Monthly, 59, 521–531, 1952.Google Scholar
  14. 14.
    W. V. O. Quine: A way to simplify truth functions. American Mathematical Monthly, 62, 627–631, 1955.Google Scholar
  15. 15.
    W. V. O. Quine: On cores and prime implicants of truth functions. American Mathematical Monthly, 66, 1959.Google Scholar
  16. 16.
    R. Reiter, J. de Kleer: Foundations of assumption-based truth maintenance systems: Preliminary report. 6th National Conference on Artificial Intelligence, 183–188, 1987.Google Scholar
  17. 17.
    J. R. Slagle, C.-L. Chang, R. C. T. Lee: A new algorithm for generating prime implicants. IEEE Transactions on Computers, C-19(4), 304–310, 1970.Google Scholar
  18. 18.
    P. Tison: Generalized consensus theory and application to the minimization of boolean functions. IEEE Transactions on Electronic Computers, EC-16(4), 446–456, 1986.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Peter Jackson
    • 1
  1. 1.McDonnell Douglas Research LaboratoriesSt. LouisUSA

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