Propositional Satisfiability (SAT) and Constraint Programming (CP) have developed as two relatively independent threads of research, cross-fertilising occasionally. These two approaches to problem solving have a lot in common, as evidenced by similar ideas underlying the branch and prune algorithms that are most successful at solving both kinds of problems. They also exhibit differences in the way they are used to state and solve problems, since SAT’s approach is in general a black-box approach, while CP aims at being tunable and programmable. This survey overviews the two areas in a comparative way, emphasising the similarities and differences between the two and the points where we feel that one technology can benefit from ideas or experience acquired

BDDs (Binary Decision Diagrams) are often used to represent Boolean expressions in hardware synthesis, hardware and software verification and numerous other applica-tions. BDD computation, implemented using tree data structures with binary nodes, is inherently memory intensive, and therefore suffers from the von Neumann memory bottleneck. This thesis examines an approach which can speed up BDD computation through compression of the graphical structure, reducing the overhead of handling memory pointers, and thereby reducing memory access latency. The novel aspect of this work is that a compression technique is used which allows BDD computation directly on the compressed data without the overheads of compression and decompression. The need for such an approach is driven by technology in two ways: the increasing discrepancy between CPU and memory speeds, and the move towards larger (64 bit) memory architectures. The work applies graph enumeration techniques to classify graph topology using a structural identifier (SID) coding table, providing the basis for algorithms which generate compressed representations. The work uses these new representations to develop algorithms which can pre-calculate results for specific graph-traversal operations in Combination lookup tables (CLT). The work distinguishes itself from other methods of reducing BDD access latency, such as index based systems, by improving spatial locality and simplifying computation at the same time.