Density of rational languages under invariant measures

Herman Goulet-Ouellet
University of Coimbra, Portugal

Date(s) : 24/10/2023   iCal
15 h 00 min - 16 h 00 min

The notion of density for languages was studied by Schützenberger in the 60s and by Hansel and Perrin in the 80s. In both cases, the authors focused on densities defined by Bernoulli measures. In this talk, I will present new results about densities of regular languages under invariant measures of minimal shift spaces. We introduce a compatibility condition which implies convergence of the density to a constant which depends only on the given rational language. This result can be seen as a form of equidistribution property. The compatibility condition can be stated either in terms of return words or of a skew product. The passage between the two forms is made more transparent using simple combinatorial tools inspired by ergodic theory and cohomology. This is joint work with Valérie Berthé, Carl-Fredrik Nyberg Brodda, Dominique Perrin and Karl Petersen. .


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