Computer and Information Science, ISSN 1913-8989, Vol. 1, No. 2, May 2008

The pioneering work of Akers (1978) on graphical representation of Boolean functions using Binary Decision Diagrams (BDDs) offered an attractive and convenient technique for simplification and manipulation of complex Boolean functions. Modification of these BDDs was suggested by Bryant (1986) and since then different types of Decision Diagrams (DDs) have been introduced by researchers (see the book written by Sasao T. and Fujita M. 1996 for detail). The graphical representation of Boolean functions using BDDs have been potentially used for simplification of complex functions (Drecher R., Dreshler N. and Gunther W. 2000; Hong Y., et. al 2000; Scholl C. et. al 2000). As a result, BDDs and its variations are being extensively used in logic design, synthesis and testing of digital circuits (Jabir A. M., Pradhan D. K., Singh A. K. Rajaprabhu T. L. 2007; Minato S. 1996; Lai Y. T., Pedram M. and Vrudhula S. B. K. 1996; Gergov J. and Meinel C. 1994; Shen A., Devadas S. and Ghosh A. 1995). However, minimization of number of BDD nodes has been of focal interest in several applications such as formal verification. Ordered Binary Decision Diagram (OBDD) is an important form of decision diagram generated by imposing ordering relation among function variables such that the resulting form is canonical and it provides more compact representation of Boolean functions (Litan L. H. and Molitor P. 2000; Wang Y., Abd-el-Barr M. and McCrosky C. 1997; Wegener I. 1994; Bryant R. E. 1992; Liaw H. T. and Lin C. S. 1992; Friedman S. J. and Supowit K. J. 1990; Bern J., Meinel C. and Slobodova A. 1996). OBDD representation along with the use of the data structures for caching intermediate computations provides a way for the efficient implementation of many Boolean operations. However, one major drawback of OBDD representation is that identification of optimal (minimal node) OBDD requires generating all n! OBDDs of n variable function. The ordering of the function variables corresponding to optimal OBDD is called optimal ordering and for which many techniques are already reported (Wegener I. 1994; Bryant R. E. 1992; Bern J., Meinel C. and Slobodova A. 1996; Drechslor R., Becker B. and Gockel N. 1996) but they are inefficient in respect of computational complexity and storage requirements.