Worst Case Reaction Time Analysis of Concurrent Reactive Programs

Reactive programs have to react continuously to their inputs. Here the time needed to react with the according output is important. While the synchrony hypothesis takes the view that the program is infinitely fast, real computations take time. Similar to the traditional Worst Case Execution Time (WCET), the Worst Case Reaction Time (WCRT) of a program determines the maximal time for one reaction. In this paper, we present an algorithm to determine the WCRT of a program written in the synchronous language Esterel. This value gives an upper bound for the execution time when the program is executed on a reactive processor. Specifically, we consider the execution of the Esterel program on the Kiel Esterel Processor (KEP), a reactive processor that can execute Esterel-like instructions. Here the WCRT directly determines an upper bound on the instruction cycles per logical tick. The WCRT also gives a guideline for the execution time when the Esterel program is compiled to software by a simulation-based approach. We have implemented the WCRT analysis algorithm as part of an Esterel compiler for the KEP and have measured an accuracy of analysis results of about 40% on average.