Mod-2-OBDD's: A Generalization of OBDD's and EXOR-Sum-of-Products

We present a data structure | the Mod{2{OBDD's that considerably extend OBDD's (ordered binary decision diagrams) as well as ESOP's (EXOR{sum{of{ products). Many Boolean function of practical interest like hidden weighted bit function, indirect storage access function, important symmetric functions have exponential size optimal OBDD's and/or ESOP's (even multilevel EXOR{expressions) but (low degree) polynomial size Mod{2{OBDD's. The manipulation of Mod{2{OBDD's is at least as eecient as the manipulation of OBDD's. Apply operation , quantiication, composition Bry86] have the same complexity as in the case of OBDD's. Moreover , since the size of a minimal Mod{2{OBDD{ representation of a Boolean function is, in general , smaller than the size of its optimal OBDD{ representation manipulation is more eecient. Moreover , EXOR{operation and complementation can be performed much better | namely in O(1) time. However, the price of O(1) time EXOR{apply operations is the canonicity of the Mod{2{OBDD{ representation. A Boolean function can have diierent reduced Mod{2{OBDD's of the same variable ordering similar to the case of mixed polarity RME's. In order to allow in spite of this fact eecient analysis of Mod{2{OBDD we present a probabilistical equivalence test (one{sided bounded error probability) for ESOP's and Mod{2{OBDD's which performs only linear many arithmetical operations. A Mod{2{OBDD{package is in preparation.