2. Definable genericity . . . . . . . . . . . . . . . . . . . . . . . . 2 2.1. Levels of class genericity . . . . . . . . . . . . . . . . . . . . . 2 2.2. Equivalents of definable genericity . . . . . . . . . . . . . . . . . 3 3. Rudimentary extensions . . . . . . . . . . . . . . . . . . . . . . 5 3.1. Two languages . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.2. Semantics . . . . . . ...

We show how to use various notions of genericity as tools in oracle creation. In particular, 1. we give an abstract definition of genericity that encompasses a large collection of different generic notions; 2. we consider a new complexity class AWPP, which contains BQP (quantum polynomial time), and infer several strong collapses relative to SP-generics; 3. we show that under additional assumpt...

Contents Introduction 5 1 Genericity in Non-Equivariant Dynamical Systems 8 1.

Abstract To each colored graph one can associate its closure in the universal space of isomorphism classes pointed graphs, and this subspace be regarded as a generalized subshift. Based on correspondence, we introduce two definitions for chaotic (colored) them analogous to Devaney’s. We show equivalence our novel chaos, proving their topological genericity various subsets space.

Modern object-oriented languages such as X10 require a rich framework for types capable of expressing valuedependency, type-dependency and supporting pluggable, application-specific extensions. In earlier work, we presented the framework of constrained types for concurrent, object-oriented languages, parametrized by an underlying constraint system C . Constraint systems are a very expressive fr...

Quasi-stable ideals appear as leading ideals in the theory of Pommaret bases. We show that quasi-stable leading ideals share many of the properties of the generic initial ideal. In contrast to genericity, quasistability is a characteristic independent property that can be effectively verified. We also relate Pommaret bases to some invariants associated with local cohomology, exhibit the existen...