Weighted finite automata: Computing with different topologies

Abstract

We use a very conventional model of computation to define unconventional computational processes. This leads to an easily computable class of real functions, however, this class is very different to those of nicely behaving real functions in a classical sense. All this is based on the fact that the topology of the unit interval is very different to that of infinite words representing numbers in that interval. In addition, the very inherent recursive structure of finite automata is central here. © 2011 Springer-Verlag Berlin Heidelberg.