Experience, generations, and limits in machine learning

Abstract

This paper extends traditional models of machine learning beyond their one-level structure by introducing previously obtained problem knowledge into the algorithm or automaton involved. Some authors studied more advanced than traditional models that utilize some kind of predetermined knowledge, having a two-level structure. However, even in this case, the model has not re ected the source and inherited properties of predetermined knowledge. In society, knowledge is often transmitted from previous generations. The aim of this paper is to construct and study algorithmic models of learning processes that utilize predetermined or prior knowledge. The models use recursive, subrecursive, and super-recursive algorithms. Predetermined knowledge includes: a text description, activity rules (e.g., for cognition), and speciÿc structured personal or social memory. Algorithmic models represent these three forms as separate structured processing systems: automata with (1) advice; (2) structured program; and (3) structured memory. That yields three basic models for learning systems: polynomially bounded turing machines, Turing machines, and inductive Turing machines of the ÿrst order.

Zeno machines and hypercomputation

“…The internal state of the machine, and that of the work tape, might again display a disconcerting resemblance to Thomson's lamp. The sets decidable by ITMs fit nicely in the arithmetic hierarchy-they are exactly all of ∆ 0 2 = Σ 0 2 ∩ Π 0 2 [23] and can solve the halting problem for Turing machines.…”

“…Solving HP for some subclass of machines but not by a machine in the subclass itself 6 is not necessarily interesting of itself. In this way, Turing's unsolvability proof encapsulates a principle which is more fundamental and interesting than the mere finding about the mechanics of TMs that is often taken to be.…”

Formularless Logic Function

“…The question how to do that is being discussed [1]. Alternative approaches- [3,4]. In the first approach we prove the existence of three types of computational learning algorithms, one of which requires a memory polynomially depending on the dimension of space.…”