Structure of undecidable problems in automata theory

Abstract

The purpose of this paper is to gain a better understanding of the structure of undecidable problems in automata theory by investigating the degree of unsolvability of these problems. This is achieved by using Turing machines with oracles to define when one undecidable problem can be reduced to another and to establish an infinite hierarchy of (equivalent) undecidable problems. This hierarchy is then used to classify well-known undecidable problems about various families of automata and formal languages and to study the relations between these problems. This approach reveals a well defined structuring of the undecidable problems and permits a more systematic study of these problems and their relation to various families of automata.