Empirical Analysis and Mathematical Representation of the Path Length Complexity in Binary Decision Diagrams

Abstract

Information about the distribution of path-lengths in a Binary Decision Diagrams (BDDs) representing Boolean functions is useful in determining the speed of hardware and software implementations of the circuit represented by these Boolean functions. This study presents expressions produced from an empirical analysis of a representative collection of Boolean functions. The Average Path Length (APL) and the Shortest Path Length (SPL) have simple behavior as function of the number of variables and the number of terms used in the construction of the Sum of Products (SOPs) in Boolean expressions. We present a generic expression that is uniformly adaptable to each curve of path-length versus number of terms over all the empirical data. This expression makes it possible to estimate the performance characteristics of a circuit without building its BDD. This approach applies to any number of variables, number of terms, or variable ordering method.

Applicability of feed-forward and recurrent neural networks to Boolean function complexity modeling

“…In general, a lot of research has been done in the estimation of combinational and sequential circuit related parameters (Bhanja, Lingasubramanian, & Ranganathan, 2005;Dunne & van der Hoeke, 2004;Nemani & Najm, 1996;Ramalingam & Bhanja, 2005) in which, the BFs play a major role. Mathematical models have been used proposed recently to model the BFC (Assi, Prasad, Mills, & El-Chouemi, 2005;Franco, 2005;Franco & Anthony, 2004). Assi, Prasad, and Beg, 2006 proposed the use of FFNNs for BFC prediction.…”

Investigating data preprocessing methods for circuit complexity models

“…The way a Boolean function is implemented directly affects the computation and memory resources. Being able to estimate the circuit complexity based on Boolean functions is useful for conducting design feasibility studies (Assi, Prasad, Mills, & El-Chouemi, 2005;Priyank, 1997). Mathematical and NN models have been used in the past for addressing complexityrelated problems (Beg, Prasad, & Beg, in press;Dunne & van der Hoeke, 2004;Franco, 2005;Franco & Anthony, 2004;Nemani & Najm, 1996;Prasad, Assi, & Beg, 2006b;Ramalingam & Bhanja, 2005;Raseen, Prasad, & Assi, 2005).…”

Binary Decision Diagrams and neural networks

“…There have been a lot of research works [13][14][15] done on the estimation of combinational and sequential circuit parameters from the exact Boolean function describing the circuit. A mathematical model to predict the complexity of Boolean functions, XOR/XNOR min-terms and the path length of BDDs using empirical fit were introduced in papers [16][17][18][19][20], and here we propose an alternative way to tackle this problem using neural networks (NNs).…”