Theory of Automata, Abstraction and Applications

Chapter
Part of the Mathematics for Industry book series (MFI, volume 5)

Abstract

We introduce computational models, such as sequential machines and automata, using the category theory. In particular, we introduce a generalized theorem which states the existence of the most efficient finite state automaton, called the minimal realization. First, we introduce set theoretical elementary models using sets and functions. We then consider a category of sequential machines which is an abstract model of finite automata. In the category theory, we consider several properties of compositions of morphisms. When we look at the category of sets and functions, we describe properties using equations of compositions of functions. Since the theory of category is a general theory, we can have many concrete properties from a general theorem by assigning it to specific categories such as sets and functions, linear space and linear transformations, etc.

Keywords

Sequential machine Automaton Category theory 

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Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Institute of Mathematics for IndustryKyushu UniversityNishiku, FukuokaJapan

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