Logarithmically regular morphisms

Efficient Algorithms for Morphisms over Omega-Regular Languages

Morphisms to finite semigroups can be used for recognizing omega-regular languages. The socalled strongly recognizing morphisms can be seen as a deterministic computation model which provides minimal objects (known as the syntactic morphism) and a trivial complementation procedure. We give a quadratic-time algorithm for computing the syntactic morphism from any given strongly recognizing morphi...

Equality sets of prefix morphisms and regular star languages

We consider equality sets of prefix morphisms, that is, sets EG(g1, g2) = {w | g1(w) = g2(w)}, where g1 and g2 are prefix morphisms. Recall that a morphism g is prefix if, for all different letters a and b, g(a) is not a prefix of g(b). We prove a rather surprising equality on families of languages, namely, that the family of regular star languages coincides with the family of languages of form...

Morphisms on infinite alphabets, countable states automata and regular sequences

In this paper, we prove that a class of regular sequences can be viewed as projections of fixed points of uniform morphisms on a countable alphabet, and also can be generated by countable states automata. Moreover, we prove that the regularity of some regular sequences is invariant under some codings.

On Logarithmically Benford Sequences

Abstract. Let I ⊂ N be an infinite subset, and let {ai}i∈I be a sequence of nonzero real numbers indexed by I such that there exist positive constants m,C1 for which |ai| ≤ C1 · i for all i ∈ I. Furthermore, let ci ∈ [−1, 1] be defined by ci = ai C1·i for each i ∈ I, and suppose the ci’s are equidistributed in [−1, 1] with respect to a continuous, symmetric probability measure μ. In this paper,...

Inference of Finite-State Transducers by Using Regular Grammars and Morphisms