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http://dx.doi.org/10.9708/jksci.2015.20.4.095

A Selection-Deletion of Prime Implicants Algorithm Based on Frequency for Circuit Minimization  

Lee, Sang-Un (Dept. of Multimedia Eng., Gangneung-Wonju National University)
Publication Information
Journal of the Korea Society of Computer and Information / v.20, no.4, 2015 , pp. 95-102 More about this Journal
Abstract
This paper proposes a simple algorithm for circuit minimization. There are currently two effective heuristics for circuit minimization, namely manual Karnaugh maps and computable Quine-McCluskey algorithm. The latter, however, has a major defect: the runtime and memory required grow $3^n/n$ times for every increase in the number of variables n. The proposed algorithm, however, extracts the prime implicants (PI) that cover minterms of a given Boolean function by deriving an implicants table based on frequency. From a set of the extracted prime implicants, the algorithm then eliminates redundant PIs again based on frequency. The proposed algorithm is therefore capable of minimizing circuits polynomial time when faced with an increase in n. When applied to various 3-variable and 4-variable cases, it has proved to swiftly and accurately obtain the optimal solutions.
Keywords
Frequency; Minterm; Implicant; Prime implicant; Essential prime implicant;
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1 V. Kabanets and J. Y. Cai, "Circuit Minimization Problem," Proceedings of 32nd Symposiumon Theory of Computing, Portland, Oregon, USA, pp. 73-79, Jun. 2000.
2 M. Karnaugh, "The Map Method for Synthesis of Combinational Logic Circuits," Transactions of the American Institute of Electrical Engineers, part I, Vol. 72, No. 9, pp. 593-599, Nov. 1953.
3 N. Sarkar, K. Petrus, and H. Hossain, "Software Implementation of theQuine-McCluskey Algorithmfor Logic GateMinimisation," Proceedings of the NACCQ, pp. 375-378, Napier, New Zealand, Jul, 2001.
4 R. K. Brayton, G. D.Hachtel, C.McMullen, andA. L. Sangiovanni-Vincentelli, "LogicMinimizationAlgorithms for VLSI Synthesis," Springer, 1984.
5 N. V. Vinodchandran, "Nondeterministic Circuit Minimization Problemand Derandomizing Arthur-MerlinGames," International Journal of Foundations of Computer Science, Vol. 16, No. 6, pp.1297-1308, Dec. 2005.   DOI   ScienceOn
6 R. Siggh, A. Arora, G. Singh, and J.Malhotra, "Circuit Minimization in VLSI Using PSO&GA Algorithms," International Journal of Engineering Trends and Technology, Vol. 3, No. 1, pp. 43-46, Feb. 2012.
7 M. Morrison and N. Ranganathan, "A Novel Optimization Method for Reversible Logic Circuit Minimization," IEEE Computer Society Annual Symposiumon VLSI (ISVLSI), pp. 182-187, Aug. 2013.
8 S. R. Petrick, "ADirect Termination of the Irredundant Forms of a Boolean Function fromthe Set of Prime Implicants," Technical Report AFCRC-TR-56-110, Air Force Cambridge Res. Center, Cambridge, MA, USA, 1956.
9 T.H. Cormen, C. E. Leiserson, R. L. Rivest, L. Ronald, andC. Stein, "Introduction toAlgorithms,"McGraw-Hill, pp. 1033-1038, 2001.
10 S. U. Lee, "An ImprovedQuine-McCluskey Algorithm for CircuitMinimization," Journal of KSCI, Vol. 19, No. 3, pp. 109-117, Mar. 2014.