Discrete-Event System Theory

Researchers: Edward A. Lee
Advisor:Edward A. Lee

This project studies models of computation and programming language semantics used for the specification and modeling of real-time and reactive electronic systems. It uses extensively the mathematics of partially ordered sets, particularly as applied to prefix orders and Scott orders. Timed discrete-event systems (those where events are globally totally ordered) are modeled in a metric space. This enables the use of standard results, such as the Banach fixed-point theorem, to study determinacy and other formal properties of systems. Untimed discrete-event systems (those where events are partially ordered) are studied using the Scott topology and complete partial orders (CPOs).

A major objective of this project is to develop a framework for studying models of computation for concurrent systems. We are particularly interested in modeling the interaction between diverse heterogeneous systems. Models of computation of interest include event-based simulation models, such as those embodied in hardware description languages, synchronous/reactive languages (Esterel, Lustre, Signal, Argos), process networks, and dataflow models.

Basic issues of Turing completeness and lambda computability, boundedness, determinacy, reachability, and liveness are studied, with emphasis on decidability and efficiency of verification and synthesis algorithms. Throughout, applications to signal processing, real-time, and reactive systems are emphasized, as are synthesis and compilation techniques amenable to such modern approaches as embedded system design, hardware/software codesign and formal verification.