NCTS(South)/ NCKU Math Colloquium
DATE	2009-12-17　16:10-17:00
PLACE	R204,2F,NCTS,NCKU
SPEAKER	Prof. Tim Boykett（Department of Algebra, Johannes Kepler Universitat Linz）
TITLE	Some Notes on Reset Words for Algebraic Automata
ABSTRACT	We look at some ideas around reset words in automata defined over algebraic structures, in particular groups. We look at separable automata over finite semigroups and groups to obtain some quite strong restrictions on how long a reset word can be and show that these are Markovian. Looking at input-output automata we concentrate upon input and output alphabets that are groups and thus form a nearring. We define a metric so we can talk about automata as topological nearrings. Booth's prime radical in $N_0({\mathbb R})$ is shown not to be prime in this nearring, but still an ideal. We will talk about *time closed* nearrings of automata and show some results connected to primeness. If time allows, I will outline some small results and ideas about rings over words and their action upon a time closed group of automata.