Reduction of OBDDs in Linear Time

Ordered binary decision diagrams (OBDDs) play an important role as data structure for Boolean functions. They are used, e.g., in the logical synthesis process, for verification and test pattern generation, and as part of CAD tools. For a given ordering of the variables and a given Boolean function f the reduced OBDD, i.e. the OBDD of minimal size, is unique (up to isomorphisms) and can be computed from any OBDD G for f of size |G| in time O(¦G¦log¦G¦). A new reduction algorithm which works in optimal linear time O(|G|) is presented.

[1]  C. Y. Lee.  Representation of switching circuits by binary-decision programs , 1959 .

[2]  Sheldon B. Akers,et al.  Binary Decision Diagrams , 1978, IEEE Transactions on Computers.

[3]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[4]  R. Ladner.  The circuit value problem is log space complete for P , 1975, SIGA.

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

[6]  Hiroshi Sawada,et al.  Minimization of binary decision diagrams based on exchanges of variables , 1991, 1991 IEEE International Conference on Computer-Aided Design Digest of Technical Papers.

[7]  Randal E. Bryant,et al.  Symbolic Manipulation of Boolean Functions Using a Graphical Representation , 1985, 22nd ACM/IEEE Design Automation Conference.

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