A conjunctively decomposed boolean representation for symbolic model checking

Abstract

A canonical boolean representation is proposed, which decomposes a function into the conjunction of a sequence of components, based on a fixed variable order. The components can be represented in OBDD form. Algorithms for boolean operations and quantification are presented allowing the representation to be used for symbolic model checking. The decomposed form has a number of useful properties that OBDD’s lack. For example, the size of conjunction of two independent functions is the sum of the sizes of the functions. The representation also factors out dependent variables, in the sense that a variable that is determined by the previous variables in the variable order appears in only one component of the decomposition. An example of verifying equivalence of sequential circuits is used to show the potential advantage of the decomposed representation over OBDD's.