In this paper we define the concept of a system function language which is a language generated by a system function. We identify system function languages with recursively enumerable sets which are non-simple and co-infinite. We then define restricted system function languages and identify them with recursive sets which are co-infinite. Finally we state and prove some independence and dependence relationships between system function languages and some of the more well-known decision problems. MSC: 03D05, 03D20, 03D25.

We introduce a novel set-intersection operator called ‘most-intersection’ based on the logical quantifier ‘most’, via natural density of countable sets, to be used in determining the majority chara...

This paper seeks to build on the extensive connections that have arisen between automata theory, combinatorics on words, fractal geometry, and model theory. Results in this paper establish a characterization for the behavior of the fractal geometry of “k-automatic” sets, subsets of $[0,1]^d$ that are recognized by Büchi automata. The primary tools for building this characterization include the entropy of a regular language and the digraph structure of an automaton. Via an analysis of the strongly connected components of such a (...) structure, we give an algorithmic description of the box-counting dimension, Hausdorff dimension, and Hausdorff measure of the corresponding subset of the unit box. Applications to definability in model-theoretic expansions of the real additive group are laid out as well. (shrink)