On nonstochastic languages and homomorphic images of stochastic languages

Using a simple method we find some nonstochastic and stochastic languages related to the Dyck sets and to the languages {wcw¦w in {a, b}∗} and {wcwR¦w in {a, b}∗}. Using the theory of uniformly distributed sequences, we present a sufficient condition for a one-letter language to be nonstochastic. Among the applications is the result that {ap¦p is a prime} is nonstochastic. We also study the images of stochastic and rational stochastic languages under nonerasing and arbitrary homomorphisms as well as their relations to some well-known families. Finally, we introduce a large class of bounded languages and show that it is contained in /of∩ (DUP) = the smallest intersection-closed AFL containing DUP = {anbn¦n in N}, which is a subfamily of /oK(/oLQ = the image of the family of rational stochastic languages under nonerasing homomorphisms.

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