We present a novel algorithm for generating state spaces of asynchronous systems using Multi–valued Decision Diagrams. In contrast to related work, we encode the next–state function of a system not as a single Boolean function, but as cross–products of integer functions. This permits the application of various iteration strategies to build a system’s state space. In particular, we introduce a new elegant strategy, called saturation, and implement it in the tool SMART. On top of usually performing several orders of magnitude faster than existing BDD–based state–space generators, our algorithm’s required peak memory is often close to the final memory needed for storing the overall state space.

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We present a new method for the symbolic construction of shortest paths in reachability graphs. Our algorithm relies on a variant of edge-valued decision diagrams that supports efficient fixed-point iterations for the joint computation of both the reachable states and their distance from the initial states. Once the distance function is known, a shortest path from an initial state to a state satisfying a given condition can be easily obtained. Using a few representative examples, we show how our algorithm is vastly superior, in terms of both memory and space, to alternative approaches that compute the same information, such as ordinary or algebraic decision diagrams.

. We present a fixpoint-analysis machine, for the efficient computation of homogeneous, hierarchical, and alternating fixpoints over regular, context-free/push-down and macro models. Applications of such fixpoint computations include intra- and interprocedural data flow analysis, model checking for various temporal logics, and the verification of behavioural relations between distributed systems. The fixpoint-analysis machine identifies an adequate (parameterized) level for a uniform treatment of all those problems, which, despite its uniformity, outperforms the `standard iteration based' special purpose tools usually by factors around 10, even if the additional compilation time is taken into account. 1 Introduction and Motivation A great number of analysis and verification problems such as abstract interpretation, data flow analysis, model checking, determination of behavioural relations between distributed systems, hardware verification and synthesis, etc., boil down to the computa...