arXiv:1805.06301physics.gen-ph
Finite Information Numbers through the Inductive Combinatorial Hierarchy
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Abstract
We report on a recent conjecture by Gisin on a restriction of physical processes in sets of finite information numbers (FIN) and further analyze the entropic constraint associated with the proposed algorithm. In the course, we provide a decomposition of binary entropies in a pair of fractal sequences as functional composites of binary digit-sum functions and we construct a unique formula and an abstract partition function for these. We also prove, based on a previously introduced tool of the inductive combinatorial hierarchies that the naturally inherited self-similarity of the resulting hierarchy of entropic sets contains equivalence classes providing unlimited symbolic series for satisfying the demand posed by the FIN conjecture.
Originally I wanted to make a point here about Interactive Computation, the strong Church-Turing hypothesis and persistent Turing Machines, however, while checking on the latest research in that area before doing so, I found the following paper: https://arxiv.org/abs/1702.06000…
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