Autonomous Programming for General Purposes: Theory

Abstract

The universal Turing Machine (TM) is a model for Von Neumann computers — general-purpose computers. A human brain, linked with its biological body, can inside-skull-autonomously learn a universal TM so that he acts as a general-purpose computer and writes a computer program for any practical purposes. It is unknown whether a robot can accomplish the same. This theoretical work shows how the Developmental Network (DN), linked with its robot body, can accomplish this. Unlike a traditional TM, the TM learned by DN is a super TM — Grounded, Emergent, Natural, Incremental, Skulled, Attentive, Motivated, and Abstractive (GENISAMA). A DN is free of any central controller (e.g., Master Map, convolution, or error back-propagation). Its learning from a teacher TM is one transition observation at a time, immediate, and error-free until all its neurons have been initialized by early observed teacher transitions. From that point on, the DN is no longer error-free but is always optimal at every time instance in the sense of maximal likelihood, conditioned on its limited computational resources and the learning experience. This paper extends the Church–Turing thesis to a stronger version — a GENISAMA TM is capable of Autonomous Programming for General Purposes (APFGP) — and proves both the Church–Turing thesis and its stronger version.