In this work we face two different problems: Reduction of finite
automata and regular languages inference. We also study the
relations existing between them.


After the introduction, in the second chapter we recall the basics
of formal language theory and we establish the notation used through
the paper.

We do the same with grammatical inference in the third chapter,
where we also describe and analyze the state of art in this field.


In the fourth chapter we discuss the problems of finite automata
minimalization and reduction and we prove one of the central results
of this work, the existence of an upper-bound of the size of
irreducible finite automata which accepts a given regular language.
We also introduce the concepts of relative irreducibility and
succinctness.

 In the
fifth chapter we discuss the concepts of quotient automata nets and
structural complexity and we introduce the concept of structural
universality. We obtain the second of the central results of this
work, which establishes that any merging states algorithm obtaining
an irreducible automata which is consistent with the input
identifies the class of regular languages in the limit.


In chapter six, we introduce the concept of subautomaton associated
to a word of a language and we describe a new family of algorithms
for inference of the class of regular languages by means of finite
automata. The complexity of them depends basically on the length of
the input words, while they are nearly linear in the number of them.

In chapter seven we describe several algorithms of the mentioned
family and we compare their behaviour with several previous
inference algorithms. Finally, chapter eight is devoted to
ennumerate the conclusions and to describe several possible ways of
future work