Reachability analysis of first-order definable pushdown systems

We study pushdown systems where control states, stack alphabet, and transition relation, instead of being finite, are first-order definable in a fixed countably-infinite structure. We show that the reachability analysis can be addressed with the well-known saturation technique for the wide class of oligomorphic structures. Moreover, for the more restrictive homogeneous structures, we are able to give concrete complexity upper bounds. We show ample applicability of our technique by presenting several concrete examples of homogeneous structures, subsuming, with optimal complexity, known results from the literature. We show that infinitely many such examples of homogeneous structures can be obtained with the classical wreath product construction.Comment: to appear in CSL'1

Categoricity in Quasiminimal Pregeometry Classes

Quasiminimal pregeometry classes were introduces by Zilber [2005a] to isolate the model theoretical core of several interesting examples. He proves that a quasiminimal pregeometry class satisfying an additional axiom, called excellence, is categorical in all uncountable cardinalities. Recently Bays et al. [2014] showed that excellence follows from the rest of axioms. In this paper we present a direct proof of the categoricity result without using excellence

Slow Conductance Relaxation in Insulating Granular Al: Evidence for Screening Effects

It is shown that the conductance relaxations observed in electrical field effect measurements on granular Al films are the sum of two contributions. One is sensitive to gate voltage changes and gives the already reported anomalous electrical field effect. The other one is independent of the gate voltage history and starts when the films are cooled down to low temperature. Their relative amplitude is strongly thickness dependent which demonstrates the existence of a finite screening length in our insulating films and allows its quantitative estimate (about 10nm at 4K). This metallic-like screening should be taken into account in the electron glass models of disordered insulators