[jws]

A functional crab computer would probably have to be built from delay insensitive logic[1]. The outputs of the gates would be of the form X and !X, where the signal (crab cluster) would appear at the appropriate output.

With regards to crab supply, I think the sufficient study of reversible computing, and in particular their charge conservation properties, would address that.

You'll still have to have a mechanism to spray bits of dead fish around to feed the thing.

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[1] http://en.wikipedia.org/wiki/Delay_insensitive_circuit

[2] http://en.wikipedia.org/wiki/Reversible_computing