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Solving Boolean Equations Using ROSOP Forms
February 1998 (vol. 47 no. 2)
pp. 171-177

Abstract—Boolean equations are important tools in digital logic. Previous algorithms for solving Boolean equations are based on the Boolean algebra of disjoint SOP forms. In this paper, we develop a new Boolean algebra with more efficient Boolean operation algorithms, called the reduced ordered SOP (ROSOP) forms, which are canonical representations. ROSOPs are closely related to the well-known OBDD data structure. The results here also show the algebraic structure of OBDDs.

[1] R.K. Brayton, G.D. Hachtel, C.T. McMullen, and A.L. Sangiovanni-Vincintelli, Logic Minimization Algorithms for VLSI Synthesis.Boston: Kluwer Academic, 1984.
[2] R.E. Bryant, "Graph-Based Algorithms for Boolean Function Manipulation," IEEE Trans. Computers, Vol. C-35, No. 8, Aug. 1986, pp. 667-690.
[3] P.P. Trabado,A. Lloris-Ruiz,, and J. Ortega-Lopera,“Solution of switching equations based on a tabular algebra,” IEEE Trans. Computers, vol. 42, no. 5, pp.591-596, May 1993.
[4] S.H. Unger,“Some additions to solution of switching equations based on a tabular algebra,” IEEE Trans. Computers, vol. 43, no. 3, pp.365-367, Mar. 1994.
[5] Y. Wang, "New Data Structures for Boolean Functions," technical report, Univ. of Saskatchewan, May 1994.
[6] Y. Wang, "Data Structures, Minimization and Complexity of Boolean Functions," PhD thesis, Univ. of Saskatchewan, 1996.
[7] P.R. Bhattacharjee,S.K. Basu, and J.C. Paul,"Translation of the problem of complete test set generation of pseudo-Boolean programming," IEEE Trans. Computers, vol. 40, pp. 864-866, July 1991.
[8] B. Krishnamurthy and J.G. Tollis, "Improved Techniques for Estimating Signal Probabilities," IEEE Trans. Computers, vol. 38, no. 7, pp. 1,041-1,045, July 1989.
[9] T. Sasao, "An Algorithm to Derive the Complement of a Binary Function with Multiple-Valued Inputs," IEEE Trans. Computers, vol. 34, no. 2, pp. 131-140, Feb. 1985.
[10] Y. Wang and C. McCrosky, "Negation Trees: A Unified Approach to Boolean Function Complementation," IEEE Trans. Computers, vol. 45, no. 5, pp. 626-630, May 1996.
[11] R.E. Bryant, "Symbolic Boolean Manipulation with Ordered Binary-Decision Diagrams," ACM Computing Surveys, vol., 24 no. 3, pp. 293-318, 1992.
[12] K.M. Butler, D.E. Ross, R. Kapur, and M.R. Mercer, "Heuristics to Compute Variable Orderings for Efficient Manipulation of Ordered Binary Decision Diagrams," Proc. 28th ACM/IEEE Design Automation Conf., pp. 417-420, 1991.
[13] S.J. Friedman and K.J. Supowit, "Finding the Optimal Variable Ordering for Binary Decision Diagrams," IEEE Trans. Computers, vol. 39, no. 5, pp. 710-713, May 1990.
[14] S. Malik, A.R. Wang, R.K. Brayton, and A. Sangiovanni-Vincentelli, Logic Verification Using Binary Decision Diagrams in a Logic Synthesis Environment Proc. IEEE Int'l Conf. Computer-Aided Design (ICCAD-88), pp. 6-9, 1988.
[15] M.R. Mercer, R. Kapur, and D.E. Ross, "Functional Approaches to Generating Orderings for Efficient Symbolic Representation," Proc. 29th ACM/IEEE Design Automation Conf, pp. 614-619, 1992.
[16] R. Rudell, "Dynamic Variable Ordering for Ordered Binary Decision Diagrams," Proc. ICCAD-93, pp. 42-47, 1993.
[17] H-T. Liaw and C-S Lin, "On the OBDD-representation of general Boolean functions," IEEE Trans. Computers, vol. 41, no. 6, pp. 661-664, June 1992.
[18] I. Wegener, "The Size of Reduced OBDD's and Optimal Read-once Branching Programs for Almost All Boolean Functions," IEEE Trans. Computers, vol. 43, no. 11, Nov. 1994
[19] R.K. Brayton, J.D. Cohen, G.D. Hachtel, B.M. Trager, D.Y.Y. Yun, "Fast Recursive Boolean Function Manipulation," Proc. ISCAS 1982, pp. 58-62, 1982.
[20] K.S. Brace, R.L. Rudell, and R.E. Bryant, Efficient Implementation of a BDD Package Proc. Design Automation Conf., pp. 40-45, 1990.

Index Terms:
Boolean algebra, operations, functions, equations, and decision diagrams, SOP forms, equation solving algorithms.
Citation:
Yuke Wang, Carl McCrosky, "Solving Boolean Equations Using ROSOP Forms," IEEE Transactions on Computers, vol. 47, no. 2, pp. 171-177, Feb. 1998, doi:10.1109/12.663763
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