7 research outputs found
GLC actors, artificial chemical connectomes, topological issues and knots
Based on graphic lambda calculus, we propose a program for a new model of
asynchronous distributed computing, inspired from Hewitt Actor Model, as well
as several investigation paths, concerning how one may graft lambda calculus
and knot diagrammatics
Zipper logic
Zipper logic is a graph rewrite system, consisting in only local rewrites on
a class of zipper graphs. Connections with the chemlambda artificial chemistry
and with knot diagrammatics based computation are explored in the article.Comment: 16 pages, 24 colour figure
Computing with Coloured Tangles
We suggest a diagrammatic model of computation based on an axiom of
distributivity. A diagram of a decorated coloured tangle, similar to those that
appear in low dimensional topology, plays the role of a circuit diagram.
Equivalent diagrams represent bisimilar computations. We prove that our model
of computation is Turing complete, and that with bounded resources it can
moreover decide any language in complexity class IP, sometimes with better
performance parameters than corresponding classical protocols.Comment: 36 pages,; Introduction entirely rewritten, Section 4.3 adde
Shaded tangles for the design and verification of quantum circuits
We give a scheme for interpreting shaded tangles as quantum circuits, with
the property that if two shaded tangles are ambient isotopic, their
corresponding computational effects are identical. We analyze 11 known quantum
procedures in this way -- including entanglement manipulation, error correction
and teleportation -- and in each case present a fully-topological formal
verification, yielding generalized procedures in some cases. We also use our
methods to identify 2 new procedures, for topological state transfer and
quantum error correction. Our formalism yields in some cases significant new
insight into how the procedures work, including a description of quantum
entanglement arising from topological entanglement of strands, and a
description of quantum error correction where errors are `trapped by bubbles'
and removed from the shaded tangle.Comment: 35 pages. A short version of this paper can be found at
arXiv:1701.03309. Final versio