Equations, Synchrony, Time, and Modes

Abstract:

The key principle behind equation-based languages is that components in a system interact with one another not by reacting to inputs to produce outputs, but rather by asserting relationships between the values of variables that they share. This principle is closely related to key principle behind synchronous-reactive (SR) languages, where the meaning of a composition of components is a fixed-point solution to a system of equations. In both cases, interactions between components is a dialog, with give and take, rather than a monolog. SR languages have been used to model discrete behaviors primarily, whereas equation-based languages, particularly Modelica, have been used to model continuous dynamics primarily. In this talk, I will show how to bridge the two.

Synchronous programs execute a sequence of (conceptually) simultaneous and instantaneous computations. Each step in the sequence is called a "tick" of a conceptual clock that governs the execution. Distinctly lacking, however, is any notion of metric or measurable time in this clock, so there is no foundation in these languages for modeling continuous dynamics. The ticks form a sequence, not a time line. In fact, a correct execution of a synchronous program (conformant with the semantics) can take as much time as it likes between ticks. The intervals need not even be constant or defined.

In this talk, I will review the principles of synchronous semantics and show how they can be extended to provide a rigorous foundation for timed systems that do have a metric notion of time. In particular, I will show how discrete-event (DE) and continuous-time models can be built on top of synchronous semantics. I will also introduce a hierarchical multiform time that allows time progress at different rates in different parts of the system, and I will show how the underlying synchronous semantics ensures determinacy and preserves causality. This multiform model of time provides a foundation for modal behaviors and hybrid systems.

Slides from the presentation

Biography:Edward A. Lee is the Robert S. Pepper Distinguished Professor and former chair of the Electrical Engineering and Computer Sciences (EECS) department at U.C. Berkeley. His research interests center on design, modeling, and simulation of embedded, real-time computational systems. He is a director of Chess, the Berkeley Center for Hybrid and Embedded Software Systems, and is the director of the Berkeley Ptolemy project. He is co-author of five books and numerous papers. He has led the development of several influential open-source software packages, notably Ptolemy and its various spinoffs. His bachelors degree (B.S.) is from Yale University (1979), his masters (S.M.) from MIT (1981), and his Ph.D. from U. C. Berkeley (1986). From 1979 to 1982 he was a member of technical staff at Bell Telephone Laboratories in Holmdel, New Jersey, in the Advanced Data Communications Laboratory. He is a co-founder of BDTI, Inc., where he is currently a Senior Technical Advisor, and has consulted for a number of other companies. He is a Fellow of the IEEE, was an NSF Presidential Young Investigator, and won the 1997 Frederick Emmons Terman Award for Engineering Education.