A trichotomy theorem for countable, stable, unsuperstable theories is proved. We develop the notion of a ‘regular ideal’ of formulas and study types that are minimal with respect to such an ideal.

We consider the question, of longstanding interest, of realizing types in regular ultrapowers. In particular, this is a question about the interaction of ultrafilters and theories, which is both coarse and subtle. By our prior work it suffices to consider types given by instances of a single formula. In this article, we analyze a class of formulas φ whose associated characteristic sequence of h...

In order to study precisely the growth of timed languages, we associate to such a language a generating function. These functions (tightly related to volume and entropy of timed languages) satisfy compositionality properties and, for deterministic timed regular languages, can be characterized by integral equations. We provide procedures for closed-form computation of generating functions for so...

We investigate regular languages on infinite alphabets where words may contain binders on names. To this end, classical regular expressions and automata are extended with binders. We prove the equivalence between finite automata on binders and regular expressions with binders and investigate closure properties and complementation of regular languages with binders.

We consider a six-dimensional solitonic string solution described by a conformal chiral null model with non-trivial N = 4 superconformal transverse part. It can be interpreted as a five-dimensional dyonic solitonic string wound around a compact fifth dimension. The conformal model is regular with the short-distance (‘throat’) region equivalent to a WZW theory. At distances larger than the compa...

Abstract For quadratic word equations, there exists an algorithm based on rewriting rules which generates a directed graph describing all solutions to the equation. regular equations – those for each variable occurs at most once side of equation we investigate properties this graph, such as bounds its diameter, size, and DAG-width, well providing some insights into symmetries in structure. As c...