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2 - Monoidal Finite-State Automata

from Part I - Formal Background

Published online by Cambridge University Press:  29 July 2019

Stoyan Mihov  and
Klaus U. Schulz
Stoyan Mihov
Affiliation:
Bulgarian Academy of Sciences
Klaus U. Schulz
Affiliation:
Ludwig-Maximilians-Universität Munchen
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Summary

As a starting point we study finite-state automata, which represent the simplest devices for recognizing languages. The theory of finite-state automata has been described in numerous textbooks both from a computational and an algebraic point of view. Here we immediately look at the more general concept of a monoidal finite-state automaton, and the focus of this chapter is general constructions and results for finite-state automata over arbitrary monoids and monoidal languages. Refined pictures for the special (and more standard) cases where we only consider free monoids or Cartesian products of monoids will be given later.

Keywords

finite-state automataregular expressionsregular languagesKleene Theoremtrimming of finite-state automataclosure properties of finite-state automata
Type
Chapter
Information
Finite-State Techniques
Automata, Transducers and Bimachines
 , pp. 23 - 42
Publisher: Cambridge University Press
Print publication year: 2019

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