Continuity and Rational Functions - Michaël Cadilhac, University of Oxford

Explore the concept of continuity in formal language theory and its application to word-to-word functions in this 47-minute lecture by Michaël Cadilhac from the University of Oxford. Delve into the robust theory surrounding the topological notion of continuity and its language-theoretic interpretation as V-continuity for word-to-word functions. Examine the decidability of V-continuity for transducers across various language classes, including periodic languages, group languages, and piecewise-testable languages. Investigate the relationship between transducer structure and continuous function computation, drawing from joint research with Olivier Carton, Andreas Krebs, Michael Ludwig, and Charles Paperman. Gain insights into formal models of computation, automata theory, and the abstraction of language classes to functions. Note that a basic understanding of automata theory is recommended for this medium-level technical presentation.

Introduction
Formal Language Theory
Lift
Continuous
Profile Network
Rational Functions
AC Zero
Technical slides
Visual conclusion
Transition structure