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Solution of Switching Equations Based on a Tabular Algebra
May 1993 (vol. 42 no. 5)
pp. 591-596

Several problems in switching theory such as automatic test pattern generation, can be exactly and elegantly investigated by using switching equations. An efficient tabular method is presented to solve these switching equations. The solutions of a given equation are compacted into a table, and a Boolean algebra is defined for these tables. The proposed procedure is based on the use of this Boolean algebra. The compactness and simplicity of the method are outstanding, and it is straightforward to implement for computer processing. The complexity of the procedure is computed, and some experimental results for a set of benchmark equations are provided in order to point out the effectiveness of this method.

[1] G. Boole,An Investigation of the Laws of Thought. London, 1854. Reprinted by Dover, New York.
[2] S. Rudeanu,Boolean Functions and Equations. Amsterdam, The Netherlands: North-Holland, 1974.
[3] S. Rudeanu, "An algebraic approach to Boolean equations,"IEEE Trans. Comput., pp. 206-207, Feb. 1974.
[4] W. Del Picchia, "A numerical algorithm for the resolution for Boolean equations,"IEEE Trans. Comput., vol. C-23, pp. 983-986, Sept. 1974.
[5] S. Svoboda, "An algorithm for solving Boolean equations,"IEEE Trans. Electron. Comput., pp. 557-559, Oct. 1963.
[6] M. R. Garey and D. S. Johnson,Computers and Intractability: A Guide to Theory of NP-Completeness. San Francisco, CA: Freeman, 1979.
[7] F. F. Sellers, M. Y. Hsiao, and L. W. Bearnson, "Analyzing errors with Boolean difference,"IEEE Trans. Comput., vol. C-17, pp. 676-683, July 1968.
[8] P. R. Bhattacharjee, S. K. Basu, and J. C. Paul, "Translation of the problem of complete test set generation to pseudo-Boolean programming,"IEEE Trans. Comput., vol. C-40, pp. 864-867, July 1991.
[9] B. Krishnamurthy and J. G. Tollis, "Improved techniques for estimating signal probabilities,"IEEE Trans. Comput., pp. 1041-1045, July 1989.
[10] J. Savir, G. S. Ditlow, and P. H. Bardell, "Random pattern testability,"IEEE Trans. Comput., pp. 79-90, Jan. 1984.
[11] F. W. Clegg, "Use of SPOOF's in the analysis of faulty logic networks,"IEEE Trans. Comput., pp. 229-234, Mar. 1973.
[12] F. W. Clegg and E. J. McCluskey, "Algebraic properties of faults in logic networks,"IEEE Comput. Soc. Repository, pp. 71-106, 1970.
[13] F. M. Hall,An Introduction to Abstract Algebra, (vol. 2). Cambridge, MA: Cambridge University Press, 1969.
[14] S. A. Cook, "The complexity of theorem-proving procedures," inProc. 3rd Annu. ACM Symp. Theory of Comput., 1971, pp. 151-158.
[15] B. Krishnamurthy, "Short proofs for tricky formulas,"Acta Inform., vol. 22, pp. 253-275, 1985.

Index Terms:
switching theory; automatic test pattern generation; switching equations; tabular method; Boolean algebra; computer processing; complexity; benchmark equations; Boolean algebra; computational complexity; switching theory.
P.P. Trabado, A. Lloris-Ruiz, J. Ortega-Lopera, "Solution of Switching Equations Based on a Tabular Algebra," IEEE Transactions on Computers, vol. 42, no. 5, pp. 591-596, May 1993, doi:10.1109/12.223678
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