montek singh comp790-084 nov 29, 2011. what is brownian motion? brownian cellular automata ◦...
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Emerging Technologies of Computation
Montek Singh
COMP790-084Nov 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
Today: Brownian Circuits
Neighborhood determines a cell’s next state
Timing:◦ synchronous◦ asynchronous
Review of Cellular Automata
Transition rules example:
Brownian Cellular Automata
Reversible: both directions possible◦ hence: “Brownian”
Linear “signal” propagation
Signal comes in from any of 3 directions◦ goes out on any of 3 directions◦ possibly same one!
Configuration 1: A “Hub”
2 horizontal signals 2 vertical signals
Configuration 2: A “Cjoin”
Allow one-way motion only◦ reverse rotation is blocked
Electronic equivalent = diode
What’s a Ratchet?
Allows one-way propagation only
Configuration 3: Ratchet
Symbolic representation:
Summary: 3 basic configurations
We need these 3 useful higher-level blocks:
What do we need?
Build using basic configurations
Build using basic configurations
Build using basic configurations
Build using basic configurations
Build using basic configurations
Build using basic configurations
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
Benefits and Challenges