On usefulness of information: Framework and NFA case

Abstract

In this paper we present a brief overview of the results of our research aimed at identifying and formalising various aspects of the notion of information, especially its usefulness, i.e., its ability to simplify a solution of a problem. We formalize the problem via decompositions of automata and present new results in the nondeterministic finite automata setting. We characterise some subfamilies of regular languages that are nondeterministically decomposable/undecomposable and exhibit an infinite sequence of regular languages that are nondeterministically undecomposable but decomposable in the deterministic finite automata setting.