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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(More)
We describe the main features of S m A r T, a software package providing a seamless environment for the logic and probabilistic analysis of complex systems. S m A r T can combine different formalisms in the same modeling study. For the analysis of logical behavior, both explicit and symbolic state-space generation techniques, as well as symbolic CTL(More)
We present new algorithms for the solution of large structured Markov models whose infinitesimal generator can be expressed as a Kronecker expression of sparse matrices. We then compare them with the shuffle-based method commonly used in this context and show how our new algorithms can be advantageous in dealing with very sparse matrices and in supporting(More)
We present a decomposition approach for the solution of large stochastic reward nets (SRNs) based on the concept of near-independence. The overall model consists of a set of submodels whose interactions are described by an import graph. Each node of the graph corresponds to a parametric SRN submodel and an arc from submodel A to submodel B corresponds to a(More)
— Stochastic Petri nets (SPNs) with generally distributed firing times can model a large class of systems, but simulation is the only feasible approach for their solution. We explore a hierarchy of SPN classes where modeling power is reduced in exchange for an increasingly efficient solution. Generalized stochastic Petri nets (GSPNs), deterministic and(More)
We present a new technique for the generation and storage of the reachability set of a Petri net. Our approach is inspired by previous work on Binary and Multi-valued Decision Diagrams but exploits a concept of locality for the effect of a transition's firing to vastly improve algorithmic performance. The result is a data structure and a set of manipulation(More)
Kronecker-based approaches have been proposed for the solution of structured GSPNs with extremely large state spaces. Representing the transition rate matrix using Kro-necker sums and products of smaller matrices virtually eliminates its storage requirements, but introduces various sources of overhead. We show how, by using a new data structure which we(More)