On the Descriptive and Algorithmic Power of Parity Ordered Binary Decision Diagrams

We present a data structure for Boolean functions, which we call Parity{OBDDs or { OBDDs, which combines the nice algorithmic properties of the well{known ordered binary decision diagrams (OBDDs) with a considerably larger descriptive power. Beginning from an algebraic characterization of the {OBDD complexity we prove in particular that the minimization of the number of nodes, the synthesis, and the equivalence test for {OBDDs, which are the fundamental operations for circuit veriication, have eecient de-terministic solutions. Several functions of pratical interest, i.e. the indirect storage access function, have exponential ODBB{size but are of polynomial size if {OBDDs are used.