Abstract. We propose a new saturation-based symbolic state-space generation algorithm for finite discrete-state systems. Based on the structure of the high-level model specification, we first disjunctively partition the transition relation of the system, then conjunctively partition each disjunct. Our new encoding recognizes identity transformations of state variables and exploits event locality, enabling us to apply a recursive fixed-point image computation strategy completely different from the standard breadth-first approach employing a global fix-point image computation. Compared to breadth-first symbolic methods, saturation has already been empirically shown to be several orders more efficient in terms of runtime and peak memory requirements for asynchronous concurrent systems. With the new partitioning, the saturation algorithm can now be applied to completely general asynchronous systems, while requiring similar or better run-times and peak memory than previous saturation algorithms.

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Abstract. Chaining can reduce the number of iterations required for symbolic state-space generation and model-checking, especially in Petri nets and similar asynchronous systems, but requires considerable insight and is limited to a static ordering of the events in the high-level model. We introduce a two-step approach that is instead fine-grained and dynamically applied to the decision diagrams nodes. The first step, based on a precedence relation, is guaranteed to improve convergence, while the second one, based on a notion of node fullness, is heuristic. We apply our approach to traditional breadth-first and saturation state-space generation, and show that it is effective in both cases.

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We consider the stationary solution of large ergodic continuous-time Markov chains (CTMCs) with a finite state space S , i.e., the computation of π as solution of π · Q = 0 subject to ∑ i ε s π[ i ] = 1, where Q coincides with transition rate matrix R except in its diagonal elements, Q [ i, i ] = - ∑ j ε s R [ i, j ].