# Algebraic structures: Computability vs Automaticity

How does one introduce computability into the study of algebraic structures,

such as groups, vector spaces, algebras? In answering this question we

provide two classical definitions. One is the notion of computable structure first

introduced by Malcev and Rabin in the early 60s. The other is the notion of

automatic structure first observed by Thurston (in the 80s) in the classes of groups, and then further developed in the general setting by Nerode and the speaker. The

presentation will be introductory with examples, motivation, and general background to the topics of both the theory of computable structures and the theory of automatic

structures.

The talk will be aimed at the general mathematics/computer science audience.