arXiv subjects
Publications and source records attributed to Avishy Y. Carmi.
Why does nature only allow nonlocal correlations up to Tsirelson's bound and not beyond? We construct a channel whose input is statistically independent of its output, but through which communication is nevertheless possible if and only if Tsirelson's bound is violated. This provides a statistical justification for Tsirelson's bound on nonlocal correlations in a bipartite setting.
A cellular automaton is presented whose governing rule is that the Kolmogorov complexity of a cell's neighborhood may not increase when the cell's present value is substituted for its future value. Using an approximation of this two-dimensional Kolmogorov complexity the underlying automaton is shown to be capable of simulating logic circuits. It is also shown to capture trianry logic described by a quandle, a non-associative algebraic structure. A similar automaton whose rule permits at times the increase of a cell's neighborhood complexity is shown to produce animated entities which can be used as information carriers akin to gliders in Conway's game of life.
Tangle machines are a topologically inspired diagrammatic formalism to describe information flow in networks. This paper begins with an expository account of tangle machines motivated by the problem of describing `covariance intersection' fusion of Gaussian estimators in networks. It then gives two examples in which tangle machines tell stories of adiabatic quantum computations, and discusses learning tangle machines from data.
We study a certain class of embedded two-foams that arise from gluing discs into ribbon torus knots along nonintersecting torus meridians. We exhibit several equivalent diagrammatic formalisms for these objects and identify several of their invariants, including a unique prime decomposition.
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.
Tangle machines are topologically inspired diagrammatic models. Their novel feature is their natural notion of equivalence. Equivalent tangle machines may differ locally, but globally they are considered to share the same information content. The goal of tangle machine equivalence is to provide a context-independent method to select, from among many ways to perform a task, the `best' way to perform the task. The concept of equivalent tangle machines is illustrated through examples in which they represent recursive computations, networks of adiabatic quantum computations, and networks of distributed information processing.
We provide an axiomatic characterization of information fusion, on the basis of which we define an information fusion network. Our construction is reminiscent of tangle diagrams in low dimensional topology. Information fusion networks come equipped with a natural notion of equivalence. Equivalent networks `contain the same information', but differ locally. When fusing streams of information, an information fusion network may adaptively optimize itself inside its equivalence class. This provides a fault tolerance mechanism for such networks.
The preceding paper constructed tangle machines as diagrammatic models, and illustrated their utility with a number of examples. The information content of a tangle machine is contained in characteristic quantities associated to equivalence classes of tangle machines, which are called invariants. This paper constructs invariants of tangle machines. Chief among these are the prime factorizations of a machine, which are essentially unique. This is proven using low dimensional topology, through representing a colour-suppressed machine as a diagram for a network of jointly embedded spheres and intervals in 4-space. The complexity of a tangle machine is defined as its number of prime factors.