Weakly almost periodic functions, model-theoretic stability, and minimality of topological groups

We investigate the automorphism groups of $\aleph\_0$-categorical structures and prove that they are exactly the Roelcke precompact Polish groups. We show that the theory of a structure is stable if and only if every Roelcke uniformly continuous function on the automorphism group is weakly almost periodic. Analysing the semigroup structure on the weakly almost periodic compactification, we show that continuous surjective homomorphisms from automorphism groups of stable $\aleph\_0$-categorical structures to Hausdorff topological groups are open. We also produce some new WAP-trivial groups and calculate the WAP compactification in a number of examples

Access Control Synthesis for Physical Spaces

Access-control requirements for physical spaces, like office buildings and airports, are best formulated from a global viewpoint in terms of system-wide requirements. For example, "there is an authorized path to exit the building from every room." In contrast, individual access-control components, such as doors and turnstiles, can only enforce local policies, specifying when the component may open. In practice, the gap between the system-wide, global requirements and the many local policies is bridged manually, which is tedious, error-prone, and scales poorly. We propose a framework to automatically synthesize local access control policies from a set of global requirements for physical spaces. Our framework consists of an expressive language to specify both global requirements and physical spaces, and an algorithm for synthesizing local, attribute-based policies from the global specification. We empirically demonstrate the framework's effectiveness on three substantial case studies. The studies demonstrate that access control synthesis is practical even for complex physical spaces, such as airports, with many interrelated security requirements

Eberlein oligomorphic groups

We study the Fourier--Stieltjes algebra of Roelcke precompact, non-archimedean, Polish groups and give a model-theoretic description of the Hilbert compactification of these groups. We characterize the family of such groups whose Fourier--Stieltjes algebra is dense in the algebra of weakly almost periodic functions: those are exactly the automorphism groups of $\aleph_0$-stable, $\aleph_0$-categorical structures. This analysis is then extended to all semitopological semigroup compactifications $S$ of such a group: $S$ is Hilbert-representable if and only if it is an inverse semigroup. We also show that every factor of the Hilbert compactification is Hilbert-representable.Comment: 23 page