Minimization of binary decision diagrams based on exchanges of variables

The authors present a novel exact algorithm and gradual improvement methods for minimizing binary decision diagrams (BDDs). In the exact minimization algorithm, the optimum order is searched by the exchanges of variables of BDDs based on the framework of the algorithm of S.J. Friedman and K.J. Supowit (1990). The use of the BDD representation of a given function and intermediate functions makes it possible to produce pruning into the method, which drastically reduces the computation cost. The authors succeeded in minimizing a 17-variable function by the use of the BDD representation of intermediate functions and the introduction of pruning. They also propose a greedy method and a simulated annealing method based on exchanges of two arbitrary variables, and a greedy method based on exchanges of adjacent m variables for m=3 and 4.<<ETX>>

[1]  Kenneth J. Supowit,et al.  Finding the Optimal Variable Ordering for Binary Decision Diagrams , 1990, IEEE Trans. Computers.

[2]  藤田 昌宏,et al.  Evaluation and Improvements of Boolean Comparison Method Based on Binary Decision Diagrams , 1988 .

[3]  Nagisa Ishiura,et al.  A Class of Logic Functions Expressible by Polynomial-Size Binary Decision Diagrams , 1991 .

[4]  Nagisa Ishiura,et al.  Shared binary decision diagram with attributed edges for efficient Boolean function manipulation , 1990, 27th ACM/IEEE Design Automation Conference.

[5]  石浦 菜岐佐,et al.  A Class of Logic Functions Expressible by a Polynomial-Size Binary Decision Diagram , 1989 .

[6]  Randal E. Bryant,et al.  Efficient implementation of a BDD package , 1991, DAC '90.

[7]  Randal E. Bryant,et al.  Graph-Based Algorithms for Boolean Function Manipulation , 1986, IEEE Transactions on Computers.

[8]  Albert R. Wang,et al.  Logic verification using binary decision diagrams in a logic synthesis environment , 1988, [1988] IEEE International Conference on Computer-Aided Design (ICCAD-89) Digest of Technical Papers.

[9]  Masahiro Fujita,et al.  Evaluation and improvement of Boolean comparison method based on binary decision diagrams , 1988, [1988] IEEE International Conference on Computer-Aided Design (ICCAD-89) Digest of Technical Papers.

[10]  Don E. Ross,et al.  Heuristics to compute variable orderings for efficient manipulation of ordered binary decision diagrams , 1991, 28th ACM/IEEE Design Automation Conference.

[11]  Kenneth J. Supowit,et al.  Finding the Optimal Variable Ordering for Binary Decision Diagrams , 1987, 24th ACM/IEEE Design Automation Conference.

[12]  Masahiro Fujita,et al.  On variable ordering of binary decision diagrams for the application of multi-level logic synthesis , 1991, Proceedings of the European Conference on Design Automation..