1. Montek Singh COMP790-084 Nov 29, 2011

2.  What is Brownian motion?  Brownian Cellular Automata ◦ Asynchronous Cellular Automata  Mapping Circuits to Brownian Cellular Automata ◦ Basic building blocks ◦ Higher-level building blocks  Benefits and Challenges

3.  Neighborhood determines a cell’s next state  Timing: ◦ synchronous ◦ asynchronous

4.  Transition rules example:

5.  Reversible: both directions possible ◦ hence: “Brownian”

6.  Signal comes in from any of 3 directions ◦ goes out on any of 3 directions ◦ possibly same one!

7.  2 horizontal signals  2 vertical signals

8.  Allow one-way motion only ◦ reverse rotation is blocked  Electronic equivalent = diode

9.  Allows one-way propagation only

10.  Symbolic representation:

11.  We need these 3 useful higher-level blocks:

18.  Possible to get around the timing/clocking problem ◦ use asynchronous cellular automata  Brownian motion desirable ◦ for backtracking ◦ possibly for exploring solution space??  How to implement? ◦ still in its infancy ◦ harness noise and fluctuations