A Fine-Grained Fullness-Guided Chaining Heuristic for Symbolic Reachability Analysis

Abstract

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.

An Efficient Fully Symbolic Bisimulation Algorithm for Non-Deterministic Systems

“…Section 3 shows how saturation may be used to compute a fixpoint of a more complex formula. We conclude this brief discussion by observing that the saturation algorithm has been enhanced algorithmically in various ways, such as employing fine-grained chaining [3]. Although such enhancements may produce additional improvement, our work uses the basic saturation heuristic described above, without additional algorithmic enhancements, to obtain the largest bisimulation of a LTS.…”

Efficient guided symbolic reachability using reachability expressions

“…"Chaining" [14,8] refers to a method that has been effectively used by Roig, Cortadella and Pastors, among others, to significantly reduce the number of fixpoint iterations in reachability analysis of asynchronous circuits and Petri-net based models. In the context of circuits, each gate has one or more inputs and an output signal.…”

Parallelising Symbolic State-Space Generators

“…The machine used for this evaluation is a dualprocessor, dual-core PC with 2GB of memory and Intel Xeon CPU 3.06GHz processors with 512KB cache sizes, running Redhat Linux AS 4, Redhat kernel 2.6.9-22.ELsmp, with glibc 2.3.4-2.13. We applied the algorithms to a set of parameterised models previously used to evaluate Saturation [3,5,6], where the parameter controls the size of a model's state space. One of our models is the Runway Safety Monitor (RSM) designed by Lockheed Martin and NASA to reduce aviation accidents [18].…”

“…However, Saturation does not dictate the order in which these events should be fired. For example, firing 0 To address this problem, we use the chaining heuristic of [3], which extracts the strongly connected components (SCCs) from a dynamic transition graph that is built from the static graph of Fig. 5 and the dynamic pattern of non-zero children of node p. We use these SCCs to enhance the order of parallel event firings.…”

“…The algorithm also uses supporting functions for creating and deleting nodes, performing a union on two nodes, storing saturated nodes by checking them into a hash table, and caching results to previous calls of Fire. Experimental results reported in [3,5,6] consistently show that Saturation outperforms breadth-first symbolic state-space generation by orders of magnitude in both memory and time, making it arguably the most efficient state-space generation algorithm for globally-asynchronous locally-synchronous discrete event systems.…”