Friday, May 12, 4PM
Hogan Room, Cory Hall


Finite State Machines and Differential Equations:
Using dynamical systems theory to understand VLSI circuits


                    Mark Greenstreet

              University of British Columbia


Digital models are powerful abstractions that enable us to implement
complicated systems on VLSI chips.  However, most digital models lack a
clear relation to more detailed circuit models.  As high performance
circuit design often depends on the analog phenomena, a mathematically
sound mapping from continuous to discrete behavior is desirable.  In
other words, when can we say that a finite state machine is implemented
by a system on differential equations?
Dynamical systems theory is a promising basis for addressing these
questions.  The talk will show how concepts such as fixed-point
attractors, periodic attractors, invariant manifolds, and separators
can be applied to understanding circuits.  Several examples, from both
self-timed and synchronous design will be presented.