Tangled circuit diagrams II

Instead of proceeding linearly with the exposition I decided today to point out an open problem.

We are able to distinguish using representations (invariants) the circuits mentioned in Tangled circuit diagrams I, but other very simple examples escape our methods (or perhaps the expressions we are trying to distinguish are actually the same and we can't see the proof).

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Tangled circuit diagrams I

I haven't blogged for some time, but I want to start a series of posts about a paper we (Rosebrugh, Sabadini and I) have written on tangled circuit diagrams (we are just cleaning up final details now). I have given hints in earlier posts but now I would like to give an exposition in blog-post form.

The aim is to describe an algebra with the property that expressions in the algebra may be pictured as circuit diagrams, but circuits in which the tangling of the wires is taken into account.

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