Application of Partial Orders to Timed Concurrent Systems

Edward A. Lee

article in Partial order techniques for the analysis and synthesis of hybrid and embedded systems,
special tutorial session organized by Domitilla Del Vecchio and George Pappas,
in Proceedings of the IEEE Conference on Decision and Control (CDC 07) , December 12-14, New Orleans, LA, United States.

Prepublished version
Published version



This tutorial focuses on system models consisting of interactive concurrent components that communicate via signals. The signals are functions that map time into values. Discrete-event, continuous-time, and hybrid systems fall in this category. This tutorial shows how signals can be viewed as elements of a partially ordered set under a prefix order, and systems can be interpreted as compositions of functions over this partially ordered set. Properties of these functions, such as monotonicity, continuity, and causality, can be used to answer questions about systems, such as liveness and existence and uniqueness of solutions. For example, Zeno behavior in hybrid systems can be studied as a liveness problem.More importantly, we can give a rigorous semantics to discrete-event, continuous-time, and hybrid systems, and we can show that synchronous/reactive systems are a simple special case where time is simply a totally ordered discrete set.