Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Quines are the Fittest Programs - Nesting Algorithmic Probability Converges to Constructors

Version 1 : Received: 27 October 2020 / Approved: 28 October 2020 / Online: 28 October 2020 (11:17:03 CET)

How to cite: Sarkar, A.; Al-Ars, Z.; Bertels, K. Quines are the Fittest Programs - Nesting Algorithmic Probability Converges to Constructors. Preprints 2020, 2020100584 (doi: 10.20944/preprints202010.0584.v1). Sarkar, A.; Al-Ars, Z.; Bertels, K. Quines are the Fittest Programs - Nesting Algorithmic Probability Converges to Constructors. Preprints 2020, 2020100584 (doi: 10.20944/preprints202010.0584.v1).

Abstract

In this article we explore the limiting behavior of the universal prior distribution obtained when applied over multiple meta-level hierarchy of programs and output data of a computational automata model. We were motivated to alleviate the effect of Solomonoff's assumption that all computable functions or hypotheses of the same length are equally likely, by weighing each program in turn by the algorithmic probability of their description number encoding. In the limiting case, the set of all possible program strings of a fixed-length converges to a distribution of self-replicating quines and quine-relays - having the structure of a constructor. We discuss how experimental algorithmic information theory provides insights towards understanding the fundamental metrics proposed in this work and reflect on the significance of these result in digital physics and the constructor theory of life.

Subject Areas

algorithmic probability; universal constructors; self-replication; universal Turing machines; algorithmic information theory; deterministic finite automaton

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