Hierarchical Set Decision Diagrams and Regular Models

This paper presents algorithms and data structures that exploit a compositional and hierarchical specification to enable more efficient symbolic model-checking. We encode the state space and transition relation using hierarchical Set Decision Diagrams (SDD) [9]. In SDD, arcs of the structure are labeled with sets, themselves stored as SDD. To exploit the hierarchy of SDD, a structured model representation is needed. We thus introduce a formalism integrating a simple notion of type and instance. Complex composite behaviors are obtained using a synchronization mechanism borrowed from process calculi. Using this relatively general framework, we investigate how to capture similarities in regular and concurrent models. Experimental results are presented, showing that this approach can outperform in time and memory previous work in this area

Algebraic Decision Diagrams and Their Applications

In this paper we present theory and experimental results on Algebraic Decision Diagrams. These diagrams extend BDDs by allowing values from an arbitrary finite domain to be associated with the terminal nodes of the diagram. We present a treatment founded in Boolean algebras and discuss algorithms and results in several areas of application: Matrix multiplication, shortest path algorithms, and direct methods for numerical linear algebra. Although we report an essentially negative result for Gaussian elimination per se, we propose a modified form of ADDs which appears to circumvent the difficulties in some cases. We discuss the relevance of our findings and point to directions for future work

A Thread-Safe Library for Binary Decision Diagrams

We describe the motivations, technical problems and solutions behind the implementation of BeeDeeDee, a new thread-safe Java library for Binary Decision Diagrams (BDDs) manipulation. BeeDeeDee allows clients to share a single factory of BDDs, in real parallelism, and reduce the memory footprint of their overall execution, at a very low synchronization cost. We prove through experiments on multi-core computers that BeeDeeDee is an effective thread-safe library for BDD manipulation. As test cases, we consider multiple instances of the n-queens problem, the construction of circuits and the parallel execution of information flow static analyses of Java programs, for distinct properties of variables. For sequential-only executions, BeeDeeDee is faster than other non-thread-safe Java libraries and as fast as non-thread-safe C libraries