Comparing hierarchies of total functionals

In this paper we consider two hierarchies of hereditarily total and continuous functionals over the reals based on one extensional and one intensional representation of real numbers, and we discuss under which asumptions these hierarchies coincide. This coincidense problem is equivalent to a statement about the topology of the Kleene-Kreisel continuous functionals. As a tool of independent interest, we show that the Kleene-Kreisel functionals may be embedded into both these hierarchies.Comment: 28 page

On the robustness of Herlihy's hierarchy

A wait-free hierarchy maps object types to levels in Z(+) U (infinity) and has the following property: if a type T is at level N, and T' is an arbitrary type, then there is a wait-free implementation of an object of type T', for N processes, using only registers and objects of type T. The infinite hierarchy defined by Herlihy is an example of a wait-free hierarchy. A wait-free hierarchy is robust if it has the following property: if T is at level N, and S is a finite set of types belonging to levels N - 1 or lower, then there is no wait-free implementation of an object of type T, for N processes, using any number and any combination of objects belonging to the types in S. Robustness implies that there are no clever ways of combining weak shared objects to obtain stronger ones. Contrary to what many researchers believe, we prove that Herlihy's hierarchy is not robust. We then define some natural variants of Herlihy's hierarchy, which are also infinite wait-free hierarchies. With the exception of one, which is still open, these are not robust either. We conclude with the open question of whether non-trivial robust wait-free hierarchies exist

Ontology-based semantic interpretation of cylindricity specification in the next-generation GPS

Cylindricity specification is one of the most important geometrical specifications in geometrical product development. This specification can be referenced from the rules and examples in tolerance standards and technical handbooks in practice. These rules and examples are described in the form of natural language, which may cause ambiguities since different designers may have different understandings on a rule or an example. To address the ambiguous problem, a categorical data model of cylindricity specification in the next-generation Geometrical Product Specifications (GPS) was proposed at the University of Huddersfield. The modeling language used in the categorical data model is category language. Even though category language can develop a syntactically correct data model, it is difficult to interpret the semantics of the cylindricity specification explicitly. This paper proposes an ontology-based approach to interpret the semantics of cylindricity specification on the basis of the categorical data model. A scheme for translating the category language to the OWL 2 Web Ontology Language (OWL 2) is presented in this approach. Through such a scheme, the categorical data model is translated into a semantically enriched model, i.e. an OWL 2 ontology for cylindricity specification. This ontology can interpret the semantics of cylindricity specification explicitly. As the benefits of such semantic interpretation, consistency checking, inference procedures and semantic queries can be performed on the OWL 2 ontology. The proposed approach could be easily extended to support the semantic interpretations of other kinds of geometrical specifications