Topological Entropy of Formal Languages
نویسندگان
چکیده
In this workwe shall consider a notion of complexity of formal languages L that is inspired by the concept of entropy from dynamical systems. More precisely, we shall define the topological entropy of L to be the exponential growth-rate of the restrictions of the Nerode congruence relation of L to words of length at most n. We shall show that the topological entropy of regular languages is always zero, but that there are also non-regular languages with vanishing entropy, for example Dyck-languages. Furthermore, we shall establish a way of how to compute the entropy of a formal language that is given by a topological automaton accepting it. Finally, we shall point out that the topological entropy of a formal language can be seen as the entropic dimension of a suitable precompact pseudo-metric space.
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Topological Entropy of Formal Languages
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