We tackle the containment problem for conjunctive queries with negation, which takes two queries q1 and q2 as input and asks if q1 is contained in q2. A general approach for solving this problem consists of considering all completions of q1 (intuitively these completions represent all canonical databases that satisfy q1) and checking if each completion yields the same answer on q2. Since the to...

We establish the following model-theoretic characterization: profinite L-structures, the cofiltered limits of finite L-structures, are retracts of ultraproducts of finite L-structures. As a consequence, any elementary class of L-structures axiomatized by L-sentences of the form ∀~x(ψ0(~x) → ψ1(~x)), where ψ0(~x), ψ1(~x) are existencialpositives L-formulas, is closed under the formation of profi...

In previous work, the first author established a natural bijection between minimal subshifts and maximal regular J -classes of free profinite semigroups. In this paper, the Schützenberger groups of such J -classes are investigated, in particular in respect to a conjecture proposed by the first author concerning their profinite presentation. The conjecture is established for all non-periodic min...

This is a survey and announcement of recent results on the structure of free profinite semigroups using techniques and results from symbolic dynamics. The intimate connection between uniformly recurrent infinite words and J -maximal regular J -classes is explored to compute the maximal subgroups of the J -classes associated with Arnoux-Rauzy infinite words, which turn out to be free profinite g...

I present highlights from a formalized development of domain theory in the theorem prover Coq. This is the first development of domain theory that is effective, formalized and that supports all the usual constructions on domains. In particular, I develop constructive models of both the unpointed profinite and the pointed profinite domains. Standard constructions (e.g., products, sums, the funct...