Model Checking

Ordered Binary-Decision Diagrams (OBDDs) represent Boolean functions as directed acyclic graphs. They form a canonical representation, making testing of functional properties such as satisfiability and equivalence straightforward. A number of operations on Boolean functions can be implemented as graph algorithms on OBDD data structures. Using OBDDs, a wide variety of problems can be solved through symbolic analysis. First, the possible variations in system parameters and operating conditions are encoded with Boolean variables. Then the system is evaluated for all variations by a sequence of OBDD operations. Researchers have thus solved a number of problems in digital-system design, finite-state system analysis, artificial intelligence, and mathematical logic. This paper describes the OBDD data structure and surveys a number of applications that have been solved by OBDD-based symbolic analysis.

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Symbolic Boolean manipulation with ordered binary-decision diagrams

The ordered binary decision diagram (OBDD) has proven useful in many applications as an efficient data structure for representing and manipulating Boolean functions. A serious drawback of OBDD's is the need for application-specific heuristic algorithms to order the variables before processing. Further, for many problem instances in logic synthesis, the heuristic ordering algorithms which have been proposed are insufficient to allow OBDD operations to complete within a limited amount of memory. The paper proposes a solution to these problems based on having the OBDD package itself determine and maintain the variable order. This is done by periodically applying a minimization algorithm to reorder the variables of the OBDD to reduce its size. A new OBDD minimization algorithm, called the sifting algorithm, is proposed and appears especially effective in reducing the size of the OBDD. Experiments with dynamic variable ordering on the problem of forming the OBDD's for the primary outputs of a combinational circuit show that many computations complete using dynamic variable ordering when the same computation fails otherwise.

Dynamic variable ordering for ordered binary decision diagrams

Pex automatically produces a small test suite with high code coverage for a .NET program. To this end, Pex performs a systematic program analysis (using dynamic symbolic execution, similar to path-bounded model-checking) to determine test inputs for Parameterized Unit Tests. Pex learns the program behavior by monitoring execution traces. Pex uses a constraint solver to produce new test inputs which exercise different program behavior. The result is an automatically generated small test suite which often achieves high code coverage. In one case study, we applied Pex to a core component of the .NET runtime which had already been extensively tested over several years. Pex found errors, including a serious issue.

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Pex: white box test generation for .NET

With the advent of portable and high-density microelectronic devices, the power dissipation of very large scale integrated (VLSI) circuits is becoming a critical concern. Accurate and efficient power estimation during the design phase is required in order to meet the power specifications without a costly redesign process. In this paper, we present a review of the power estimation techniques that have recently been proposed. >

A survey of power estimation techniques in VLSI circuits

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 canonical form in the ROBDD, and memory use is improved by merging the hash table and the ROBDD into a hybrid data structure A memory function 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 recycling 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

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Karl S. Brace

Papers

Efficient implementation of a BDD package