Abstract
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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References
R. H. Brayton, G. D. Hachtel, C. T. McMullen, A. L. Sangiovanni-Vincentelli: Logic Minimization Algorithms for VLSI Synthesis. Boston, MA: Kluwer-Academic, 1984.
T. Dean, M. Boddy: An analysis of time-dependent planning. 7th AAAI, 49–54, 1988.
E. Eder: Consolution and its relation with resolution. 12th IJCAI, 132–136, 1991.
P. Jackson: The SLOOP Manual. Artificial Intelligence Applications Institute, Edinburgh University, 1987.
P. Jackson: Computing prime implicates. Proceedings 20th Annual Computer Science Conference, 65–72, New York: ACM Press, 1992.
P. Jackson: Computing minimal refutations. Proceedings of 3rd Scandinavian Conference on Artificial Intelligence, 107–118, Amsterdam: IOS Press, 1991.
P. Jackson: Possibilistic prime implicates and their use in abduction. Proceedings of AAAI-91 Workshop on Abduction, 44–50, 1991.
P. Jackson, J. Pais: Computing prime implicants. Proceedings of 10th International Conference on Automated Deduction, 543–557, 1990.
A. Kean, Tsiknis, G: An incremental method for generating prime implicants/ implicates. J. Symb. Comp., 9, 185–206, 1990.
E. L. McCluskey Jr: Minimization of Boolean functions. Bell Systems Technical Journal, 35, 1417–1444, 1956.
S. Muroga: Logic Design and Switching Theory. New York, NY: Wiley, 1979.
J. Pais, P. Jackson: Partial monotonicity and a new version of the Ramsey Test To appear in Studia Logica.
W. V. O. Quine: The problem of simplifying truth functions. American Mathematical Monthly, 59, 521–531, 1952.
W. V. O. Quine: A way to simplify truth functions. American Mathematical Monthly, 62, 627–631, 1955.
W. V. O. Quine: On cores and prime implicants of truth functions. American Mathematical Monthly, 66, 1959.
R. Reiter, J. de Kleer: Foundations of assumption-based truth maintenance systems: Preliminary report. 6th National Conference on Artificial Intelligence, 183–188, 1987.
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.
P. Tison: Generalized consensus theory and application to the minimization of boolean functions. IEEE Transactions on Electronic Computers, EC-16(4), 446–456, 1986.
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© 1992 Springer-Verlag Berlin Heidelberg
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Jackson, P. (1992). Computing prime implicates incrementally. In: Kapur, D. (eds) Automated Deduction—CADE-11. CADE 1992. Lecture Notes in Computer Science, vol 607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55602-8_170
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DOI: https://doi.org/10.1007/3-540-55602-8_170
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