The advent of increasingly dense and fast Very Large Scale Integrated (VLSI) circuits allows for the design of larger and more sophisticated digital logic circuits. Efficient logic representations are necessary for the synthesis, testing and verification of these circuits. This thesis introduces a new logic representation, called the Free Boolean Diagram (FBD). This representation can be manipu...

Most propagation-based set constraint solvers approximate the set of possible sets that a variable can take by upper and lower bounds, and perform so-called set bounds propagation. However Lagoon and Stuckey have shown that using reduced ordered binary decision diagrams (ROBDDs) one can create a practical set domain propagator that keeps all information (possibly exponential in size) about the ...

Pseudo-Boolean constraints are omnipresent in practical applications, and thus a significant effort has been devoted to the development of good SAT encoding techniques for them. Some of these encodings first construct a Binary Decision Diagram (BDD) for the constraint, and then encode the BDD into a propositional formula. These BDD-based approaches have some important advantages, such as not be...

This paper contains an experimental study of the impact of the construction strategy of reduced, ordered binary decision diagrams (ROBDDs) on the average-case computational complexity of random 3-SAT, using the CUDD package. We study the variation of median running times for a large collection of random 3-SAT problems as a function of the density as well as the order (number of variables) of th...

UNLABELLED Biological networks, such as genetic regulatory networks, often contain positive and negative feedback loops that settle down to dynamically stable patterns. Identifying these patterns, the so-called attractors, can provide important insights for biologists to understand the molecular mechanisms underlying many coordinated cellular processes such as cellular division, differentiation...

Reduced Ordered Binary Decision Diagram (ROBDD) is the most popular data structure for efficient representation and manipulation of Boolean functions. However, this novel data structure is very sensitive to the variable ordering, i.e. the size may vary from linear to exponential. Since finding the optimal variable ordering is an NP-complete problem and the best known algorithm has exponential r...

The subject of groundness analysis for (constraint) logic programs has been widely studied, and interesting domains have been proposed. Pos has been recognized as the most suitable domain for capturing the kind of dependencies arising in groundness analysis. Its (by now standard) implementation is based on reduced ordered binary-decision diagrams (ROBDDs), a well-known symbolic representation f...

Mathematical Morphology (MM) is a general framework for studying mappings between complete lattices. In particular, mappings between binary images that are translation invariant and locally defined within a window are of special interest in MM. They are called W-operators. A key aspect of MM is the representation of W-operators in terms of dilations, erosions, intersection, union, complementati...

In this paper, we present several techniques for modeling and formal verification of the Fairisle asynchronous transfer mode (ATM) switch fabric using multiway decision graphs (MDG’s). MDG’s represent a new class of decision graphs which subsumes Bryant’s reduced ordered binary decision diagrams (ROBDD’s) while accommodating abstract sorts and uninterpreted function symbols. The ATM device we i...

The subject of groundness analysis for (constraint) logic programs has been widely studied, and interesting domains have been proposed. Pos has been recognized has the most suitable domain for capturing the kind of dependencies arising in groundness analysis. Its (by now standard) implementation is based on reduced ordered binary-decision diagrams (ROBDDs), a well-known symbolic representation ...