Evaluating the output probability of Boolean functions without floating point operations

• Published in: Conference proceedings - Canadian Conference on Electrical and Computer Engineering Vol. 1; pp. 433 - 437 vol.1
• Main Authors: Yingtao Jiang, Yihui Tang, Yuke Wang, Savaria, Y.
• Format: Conference Proceeding Journal Article
• Language: English
• Published: IEEE 1999
• Subjects: Arithmetic; Boolean functions; Computational complexity; Data structures; Input variables; Integrated circuit interconnections; Logic circuits; Power generation; Probability; Testing
• ISBN: 0780355792; 9780780355798
• ISSN: 0840-7789; 2576-7046
• DOI: 10.1109/CCECE.1999.807237

Recently, two algorithms (M.A. Thornton and V.S.S. Nair, IEEE Trans. Computer-Aided Design, Vol. 14, pp. 1328-1341, 1995 ; D.M. Miller, IEEE Trans. Computer-Aided Design, Vol. 17, pp. 1328-1341, 1998) have been proposed to calculate the output probability of a Boolean function represented by an OBDD (ordered binary decision diagram). Both algorithms assume that (1) the input variables are equi-probable, and (2) each variable is statistically independent from the others. Under these assumptions, we point out that calculating the output probability is actually identical to computing the number of min-terms of the corresponding Boolean functions. Therefore, simple integer arithmetic (as opposed to the floating point arithmetic involved in Thornton et al.'s and Miller's algorithms) and logic shifts are sufficient to compute the output probability of a Boolean function represented by an OBDD. To compute the output probability of the Boolean functions represented by an OBDD with compacted edge negation, a generalized counting algorithm is also proposed.