BDD minimization using symmetries

Generalized Boolean symmetries through nested partition refinement

“…9 shows the routine that checks for a functional conflict in an OPP. This routine searches the database of simulation pairs for two consistent input vectors (lines [1][2][3][4][5][6][7][8][9][10][11][12][13]. Suppose that it finds input vectors P and Q consistent with regard to the OPP, and suppose that P, R and Q, U are the simulation pairs that correspond to P and Q.…”

“…10 shows an example of learning when refinement is disabled. 3 For this example, our algorithm encounters functional conflicts at nodes (4) and (6). While backtracking from node (6), it finds that node (5) has a functional conflict under simulation pairs Γ3 and Γ4.…”

“…Most existing symmetry-detection algorithms for Boolean functions only look for classical symmetries, i.e., symmetries that include just a single swap of variables [5], [3]. As the number of such symmetries is at most quadratic in the number of a function's inputs, they can be evaluated one by one and explicitly enumerated.…”

Constructive library-aware synthesis using symmetries

“…For completely specified functions they form a transitivity relation which can be utilized for the efficient construction of groups of more than two symmetric variables in quadratic run time. Methods for the efficient identification of variable symmetries using binary decision diagrams [3] have recently been described in [10] and [15].…”

An Efficient Method for Generating Optimal OBDD of Boolean Functions

“…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).…”