An essential element of the theory of rational languages is the link between them, finite automata, and finite monoids. The success of this relationship comes mostly from the fact that the structures involved are finite. However, when we try to expand this theory to more general languages, such as context-free and context-sensitive languages, the structures are no longer finite and so the strength of this relationship is lost. A different approach to this theory is to consider topological automata instead of automata. A topological automaton can be seen as a special case of a dynamical system. Every language admits a minimal topological automaton that recognizes it, and when we restrict ourselves to rational languages we are reduced to the already known finite case. In this seminar, I will give a brief introduction to topological automata and show some characterizations and some examples of minimal topological automata.
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