Exact Minimization of Multiple-Valued Functions for PLA Optimization
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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  Also, a detailed comparison with McBoole  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.
- R. Brayton, C. McMullen, G. Hachtel, and A. Sangiovanni-Vincentelli. Logic Minimization Algorithms for VLSI Synthesis. Springer Science+Business Media New York, 1984. CrossRef
- 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. CrossRef
- R. Brayton et al. Fast Recursive Boolean Function Manipulation. In Proceedings International Symposium on Circuits and Systems (ISCAS), page 58, May 1982.
- H. Fleisher and L. Maissel. An Introduction to Array Logic. IBM Journal of Research and Development, 19:98–109, March 1975. CrossRef
- 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.
- 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. CrossRef
- E. McCluskey. Minimization of Boolean Functions. Bell System Technical Journal, 35:1417–1444, April 1956.
- W. Quine. The Problem of Simplifying Truth Functions. American Mathematical Monthly, 59:521–531, 1952. CrossRef
- J. Roth. Computer Logic, Testing, and Verification. Computer Science Press, 1981.
- R. Rudell. Multiple-Valued Logic Minimization for PLA Synthesis. Master’s thesis, University of California, Berkeley, June 1986. Memorandum UCB/ERL M86/65.
- 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.
- 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.
- T. Sasao. Input Variable Assignment and Output Phase Optimization of PLA’s. IEEE Transactions on Computers, C-33:879–894, October 1984. CrossRef
- T. Sasao. Tautology Checking Algorithms for Multiple-Valued Input Binary Functions and Their Application. In Proceedings 14th International Symposium on Multiple-Valued Logic, 1984.
- 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. CrossRef
- T. Sasao. Personal Communication, 1986.
- Y. H. Su and P. T. Chueng. Computer Minimization of Multi-Valued Switching Functions. IEEE Transactions on Computers, C-21:995–1003, 1972. CrossRef
- P. Tison. Generalization of Consensus Theory and Application to the minimization of Boolean Functions. IEEE Transactions on Computers, C-16:446, August 1967.
- Exact Minimization of Multiple-Valued Functions for PLA Optimization
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- The Best of ICCAD
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- 20 Years of Excellence in Computer-Aided Design
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- Part III
- pp 205-216
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- Springer Science+Business Media New York
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