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

Constraint Logic Programming (CLP) is a merger of two declarative paradigms: constraint solving and logic programming. Although a relatively new field, CLP has progressed in several quite different directions. In particular, the early fundamental concepts have been adapted to better serve in different areas of applications. In this survey of CLP, a primary goal is to give a systematic description of the major trends in terms of common fundamental concepts. The three main parts cover the theory, implementation issues, and programming for applications.

Constraint logic programming : A survey

The Prolog III programming language extends Prolog by redefining the fundamental process at its heart: unification. This article presents the specifications of this new language and illustrates its capabilities.

An introduction to Prolog III

New algorithms for fault trees analysis

Embedding boolean expressions into logic programming

Unification in commutative idempotent monoids

Unification in the data structure sets

In a recent paper A. Herold and J. Siekmann generalize ‘pure’ AC unification to terms containing additional function symbols. Generalized AC unification thus attains practical relevance for a broad range of applications. Pure AC unification is used as a basic mechanism and it is this key role that has motivated our research. We have improved upon earlier approaches by basing (pure) AC unification on a firm theoretical basis and presenting algorithms which fully exploit the properties of the underlying mathematical structure. In particular, the high degree of parallelism for AC unification will become apparent. Our algorithms have been designed for parallel hardware but still yield significant improvements over earlier algorithms when used in the sequential mode.

Unification in datastructure multisets

Unification in algebras is widely seen as a means of improving the expressiveness and efficiency of resolution based deduction. In particular, finite algebras have recently gained considerable attention. Unification in the sense of Plotkin is based upon the notion of a set of most general unifiers, which however might either not exist or — at the other extreme — be too large. As a remedy to these conceptual drawbacks we suggest a redefinition of unification, such that with respect to this view unification in finite algebras becomes unitary. Previous work on unification in Postalgebras provides a universal unification algorithm. We will add a more application oriented approach. Applications of our methods to the switch level design of digital circuits are indicated.

Wolfram Büttner

Papers

Embedding boolean expressions into logic programming

Unification in commutative idempotent monoids

Unification in the data structure sets

Unification in datastructure multisets

Unification in Finite Algebras is Unitary (