An algorithm for exact bounds on the time separation of events in concurrent systems

Abstract

Determining the time separation of events is a fundamental problem in the analysis, synthesis, and optimization of concurrent systems. Applications range from logic optimization of asynchronous digital circuits to evaluation of execution times of programs for real-time systems. We present an e cient algorithm to nd exact (tight) bounds on the separation time of events in an arbitrary process graph without conditional behavior. The algorithm is based on a functional decomposition technique that permits the implicit evaluation of an in nitely unfolded process graph.

An efficient algorithm for time separation of events in concurrent systems

“…Our tool shows significant improvement in runtime over a previous exact method [8] in cases where the latter requires a large amount of graph unfolding. Compared to the heuristic tool from [4], the proposed approach provides more accurate results in some cases.…”

“…Compared to previous exact methods [8], our approach has low computational complexity, while the previous approach has no clear complexity bound. Our approach is also significantly more efficient multiple TSE queries on the same graph: basic analysis of the system is performed only once, and then TSE's between different pairs of events can be obtained with little additional cost, whereas [8] performs the analysis (and therefore the unfolding) from scratch for each TSE query on the same graph. Compared to previous heuristic methods [4], the proposed approach can handle a larger class of designs.…”

“…A set of benchmarks has been run on the prototype tool, as well as on those from [4] and [8]. Our tool shows significant improvement in runtime over a previous exact method [8] in cases where the latter requires a large amount of graph unfolding.…”

“…Like [4], [8] and [9], the approach proposed in this paper applies to decision-free cyclic systems, and like [8], it gives exact bounds for systems operating under the max-causality rule. However, there is an important difference in the methods: while previous approaches are based on graph unfolding, which performs a symbolic execution of the system until the desired TSE number finally converges, the proposed approach entirely avoids graph unfolding.…”

“…Chakraborty et al [4] proposed a heuristic method to give approximate bounds for cyclic systems operating under both max-and min-causality rules. Hulgaard et al [8] gave exact bounds on TSE's for cyclic systems operating under the max-causality rule. In [9], Hulgaard extended his approach to handle also systems with linear timing constraints.…”