• Piergiulio Corsini
  • Violeta Leoreanu
Part of the Advances in Mathematics book series (ADMA, volume 5)


The definition of an automaton, we shall present here, has its origins in a paper of Kleene (1956). The title “Representation of events in nerve sets and finite automata” of Kleene’s paper gives an idea of its motivation.

The concept of automaton had led to important results, both in mathematics and in theoretical computer science.

Automata are in fact very familiar objects, in the shape of coin machines.

The last twenty years have developed a body of research known ùnder the names of Automaton Theory and Formal Language Theory.

We mention Biology between the fields which have significant connections with Automaton Theory.

Here, we have presented the connections of Automaton Theory and Language Theory with another field, known as Hyperstructure Theory.

Using tools and methods of Hyperstructure Theory, G. G. Massouros gave a new proof of the famous Kleene’s Theorem, which states that:

„A subset of the set of words M* is acceptable from an automaton ℳ if and only if it is defined by a regular expression.”


Transitive Closure Familiar Object Language Theory Neutral Element Automaton Theory 
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Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • Piergiulio Corsini
    • 1
  • Violeta Leoreanu
    • 2
  1. 1.Department of Mathematics and Computer SciencesUniversity of UdineUdineItaly
  2. 2.Faculty of Mathematics“AI.I Cuza” UniversityIaşiRomania

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