Application of kolmogorov complexity to inductive inference with limited memory

Abstract

We consider inductive inference with limited memory[1].

We show that there exists a set U of total recursive functions such that

• U can be learned with linear long-term memory (and no short-term memory);

• U can be learned with logarithmic long-term memory (and some amount of short-term memory);

• if U is learned with sublinear long-term memory, then the short-term memory exceeds arbitrary recursive function.

Thus an open problem posed by Freivalds, Kinber and Smith[1] is solved. To prove our result, we use Kolmogorov complexity.

The author was supported by Latvian Science Council Grant No.93.599, Riga Institute of Information Technology, and scholarship ”SWH izglītībai, zinātnei un kultūrai” from Latvian Education Foundation.