Efficient implementation of a BDD package

Abstract

Efficient manipulation of Boolean functions is an important component of many computer-aided design tasks. This paper describes a package for manipulating Boolean functions based on the reduced, ordered, binary decision diagram (ROBDD) representation. The package is based on an efficient implementation of the if-then-else (ITE) operator. A hash table is used to maintain a strong carwnical form in the ROBDD, and memory use is improved by merging the hash table and the ROBDD into a hybrid data structure. A memory funcfion for the recursive ITE algorithm is implemented using a hash-based cache to decrease memory use. Memory function efficiency is improved by using rules that detect. when equivalent functions are computed. The usefulness of the package is enhanced by an automatic and low-cost scheme for rec:ycling memory. Experimental results are given to demonstrate why various implementation trade-offs were made. These results indicate that the package described here is significantly faster and more memory-efficient than other ROBDD implementations described in the literature.

Streaming BDD manipulation

“…In our format, we do not need an explicit notation of the input variable for each node because the context of the parentheses indicates the corresponding variable. 3 In Fig. 7 2.…”

“…Binary Decision Diagrams (BDDs) [4] are now commonly used for handling Boolean functions because of their superior efficiency in terms of time and space. A number of BDD packages (e.g., [3], [15], [23], [11], [22], [7]) have been implemented and successfully applied to many real-life problems.…”

Proof theory of many-valued logic--linear optimization--logic design: connections and interactions

“…A typical example of this situation are Go¨del's connectives (see (7,8) and Fig. 6) which are not continuous.7 To represent them strict linear inequalities or linear disequations are needed.…”

“…Moreover, insertion of new formulas and combination of BDDs can be done quickly as well. There exist very efficient packages for BDD manipulation [7] whose use is quite popular in logic design, see e.g. [12].…”

Decomposition techniques for efficient ROBDD construction

“…The ITE method [3] for constructing t~OBDDs is similar; there are equivalent ITE operators for apply and compose. For details on ROBDDs, and the implementation of a typical ROBDD package, please refer to [4,5,3].…”