Efficient Boolean manipulation with OBDD's can be extended to FBDD's

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Abstract
OBDD's are the state-of-the-art data structure for Boolean function manipulation. Basic tasks of Boolean manipulation such as equivalence test, satisfiability test, tautology test and single Boolean synthesis steps can be performed efficiently in terms of fixed ordered OBDD's. The bottleneck of most OBDD-applications is the size of the represented Boolean functions since the total computation merely remains tractable as long as the OBDD-representations remain of reasonable size. Since it is well known that OBDD's are restricted FBDD's (free BDD's, i.e., BDD's that test, on each path, each input variable at most once), and that FBDD-representations are often much more (sometimes even exponentially more) concise than OBDD-representations. We propose to work with a more general FBDD-based data structure. We show that FBDD's of a fixed type provide, similar as OBDD's of a fixed variable ordering, canonical representations of Boolean functions, and that basic tasks of Boolean manipulation can be performed in terms of fixed typed FBDD's similarly efficient as in terms of fixed ordered OBDD's. In order to demonstrate the power of the FBDD-concept we show that the verification of the circuit design for the hidden weighted bit function proposed Bryant can be carried out efficiently in terms of FBDD's while this is, for principal reasons, impossible in terms of OBDD's.

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