Exact Minimization of Multiple-Valued Functions for PLA Optimization

  • R. Rudell
  • A. Sangiovanni-Vincentelli

Abstract

We present an algorithm for determining the minimum representation of an incompletely-specified, multiple-valued input, binary-valued output, function. The overall strategy is similar to the well-known Quine-McCluskey algorithm; however, the techniques used to solve each step are new. The advantages of the algorithm include a fast technique for detecting and eliminating from further consideration the essential prime implicants and the totally redundant prime implicants, and a fast technique for generating a reduced form of the prime implicant table. The minimum cover problem is solved with a branch and bound algorithm using a maximal independent set heuristic to control the selection of a branching variable and the bounding. Using this algorithm, we have derived minimum representations for several mathematical functions whose unsuccessful exact minimization has been previously reported in the literature. The exact algorithm has been used to determine the efficiency and solution quality provided by the heuristic minimize Espresso-MV [11] Also, a detailed comparison with McBoole [2] shows that the algorithm presented here is able to solve a larger percentage of the problems from a set of industrial examples within a fixed allocation of computer resources.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    R. Brayton, C. McMullen, G. Hachtel, and A. Sangiovanni-Vincentelli. Logic Minimization Algorithms for VLSI Synthesis. Springer Science+Business Media New York, 1984.MATHCrossRefGoogle Scholar
  2. [2]
    M. Dagenais, V. Agarwal, and N. Rumin. McBoole: A New Procedure for Exact Logic Minimization. IEEE Transactions on Computer-Aided Design, C-33:229–238, January 1986.CrossRefGoogle Scholar
  3. [3]
    R. Brayton et al. Fast Recursive Boolean Function Manipulation. In Proceedings International Symposium on Circuits and Systems (ISCAS), page 58, May 1982.Google Scholar
  4. [4]
    H. Fleisher and L. Maissel. An Introduction to Array Logic. IBM Journal of Research and Development, 19:98–109, March 1975.CrossRefGoogle Scholar
  5. [5]
    G. Hachtel, A. R. Newton, and A. Sangiovanni-Vincentelli. An Algorithm for Optimal PLA Folding. IEEE Transactions on Computer-Aided Design, pages 63–76, January 1982.Google Scholar
  6. [6]
    S. Hong, R. Cain, and D. Ostapko. MINI: A Heuristic Approach for Logic Minimization. IBM Journal of Research and Development, 18:443–458, September 1974.MathSciNetMATHCrossRefGoogle Scholar
  7. [7]
    E. McCluskey. Minimization of Boolean Functions. Bell System Technical Journal, 35:1417–1444, April 1956.MathSciNetGoogle Scholar
  8. [8]
    W. Quine. The Problem of Simplifying Truth Functions. American Mathematical Monthly, 59:521–531, 1952.MathSciNetMATHCrossRefGoogle Scholar
  9. [9]
    J. Roth. Computer Logic, Testing, and Verification. Computer Science Press, 1981.Google Scholar
  10. [10]
    R. Rudell. Multiple-Valued Logic Minimization for PLA Synthesis. Master’s thesis, University of California, Berkeley, June 1986. Memorandum UCB/ERL M86/65.Google Scholar
  11. [11]
    R. Rudell and A. Sangiovanni-Vincentelli. Espresso-MV: Algorithms for Multiple-Valued Logic Minimization. In Proceedings Custom Integrated Circuits Conference (CICC), pages 230–234, May 1985.Google Scholar
  12. [12]
    T. Sasao. An Application of Multiple-Valued Logic to a Design of Programmable Logic Arrays. In Proceedings 8th International Symposium on Multiple-Valued Logic, 1978.Google Scholar
  13. [13]
    T. Sasao. Input Variable Assignment and Output Phase Optimization of PLA’s. IEEE Transactions on Computers, C-33:879–894, October 1984.MathSciNetCrossRefGoogle Scholar
  14. [14]
    T. Sasao. Tautology Checking Algorithms for Multiple-Valued Input Binary Functions and Their Application. In Proceedings 14th International Symposium on Multiple-Valued Logic, 1984.Google Scholar
  15. [15]
    T. Sasao. An Algorithm to Derive the Complement of a Binary Function with Multiple-Valued Inputs. IEEE Transactions on Computers, C-34:131–140, February 1985.MathSciNetCrossRefGoogle Scholar
  16. [16]
    T. Sasao. Personal Communication, 1986.Google Scholar
  17. [17]
    Y. H. Su and P. T. Chueng. Computer Minimization of Multi-Valued Switching Functions. IEEE Transactions on Computers, C-21:995–1003, 1972.CrossRefGoogle Scholar
  18. [18]
    P. Tison. Generalization of Consensus Theory and Application to the minimization of Boolean Functions. IEEE Transactions on Computers, C-16:446, August 1967.Google Scholar

Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • R. Rudell
    • 1
  • A. Sangiovanni-Vincentelli
    • 1
  1. 1.University of CaliforniaBerkeleyUSA

Personalised recommendations