Montek Singh COMP Nov 29, 2011

 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

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

 Transition rules example:

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

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

 2 horizontal signals  2 vertical signals

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

 Allows one-way propagation only

 Symbolic representation:

 We need these 3 useful higher-level blocks:

 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