A General Notion of Useful Information

TL;DR

This paper introduces a unified framework for defining the concept of 'depth' in sequences, encompassing all existing notions from complexity theory, and reviews classical results related to these depth measures.

Contribution

It presents a comprehensive, general framework for sequence depth that unifies and captures all prior complexity-theoretic depth notions, providing a broad perspective.

Findings

Framework captures all known depth notions

Unifies various complexity-theoretic depth concepts

Reviews classical results on sequence depth

Abstract

In this paper we introduce a general framework for defining the depth of a sequence with respect to a class of observers. We show that our general framework captures all depth notions introduced in complexity theory so far. We review most such notions, show how they are particular cases of our general depth framework, and review some classical results about the different depth notions.