An efficient algorithm for time separation of events in concurrent systems

Abstract

Abstract-The time separation of events (TSE) problem is that of finding the maximum and minimum separation between the times of occurrence of two events in a concurrent system. It has applications in the performance analysis, optimization and verification of concurrent digital systems. This paper introduces an efficient polynomial-time algorithm to give exact bounds on TSE's for choice-free concurrent systems, whose operational semantics obey the max-causality rule. A choicefree concurrent system is modeled as a strongly-connected marked graph, where delays on operations are modeled as bounded intervals with unspecified distributions. While previous approaches handle acyclic systems only, or else require graph unfolding until a steady-state behavior is reached, the proposed approach directly identifies and evaluates the asymptotic steady-state behavior of a cyclic system via a graph-theoretical approach. As a result, the method has significantly lower computational complexity than previously-proposed solutions. A prototype CAD tool has been developed to demonstrate the feasibility and efficacy of our method. A set of experiments have been performed on the tool as well as two existing tools, with noticeable improvement on runtime and accuracy for several examples.

Timing Driven Placement for Quasi Delay-Insensitive Circuits

“…However, unlike in clocked systems, where all of the events at the "top" of this DAG are activated at the same time (the beginning of the clock cycle), and all events at the "bottom" commit at the same time (end of the clock cycle), asynchronous circuits do not have such alignments. Additionally, it is incorrect to approximate the system in this way, as the schedule of marked events can drastically affect the time separation of later events [20].…”

Throughput Analysis of Data-driven Asynchronous Pipelines via Event-driven Simulation

“…The throughput of an asynchronous pipeline can be modeled by the average time separation of events (TSE) [6]. Based on the traces obtained from the timing simulation, the TSEs of an asynchronous circuit can be calculated directly.…”

“…However, methods based on theoretical analysis [5][6], graph unfolding [7] and Markov analysis [8] handle only choice-free or data-independent asynchronous pipelines. A canopy graph based approach was proposed that achieves both accurate in throughput estimation and fast in runtimes [9].…”

Automated Microarchitectural Exploration for Achieving Throughput Targets in Pipelined Asynchronous Systems

“…The closed-form solutions, on the other hand, only apply to a limited set of specialized architectures (e.g., rings, meshes, and linear and simple fork-join pipelines). Recently, a graph-theoretic approach was proposed that avoids graph unfolding to achieve quite fast runtimes [16]. However, all of the aforementioned approaches that are not simulation-based cannot handle systems with choice, thereby limiting their applicability to systems without conditionals or data-dependent loops.…”