We generalize the construction of the formal ball model for metric spaces due to A. Edalat and R. Heckmann to obtain computational models for separated Q-categories. We fully describe (a) Yoneda complete and (b) continuous Yoneda complete Q-categories via their formal ball models. Our results yield solutions to two open problems in the theory of quasi-metric spaces: we show that (a) a quasi-met...

We consider smeared zeta functions and heat-kernel coefficients on the bounded, generalized cone in arbitrary dimensions. The specific case of a ball is analysed in detail and used to restrict the form of the heat-kernel coefficients A n on smooth manifolds with boundary. Supplemented by conformal transformation techniques, it is used to provide an effective scheme for the calculation of the A ...

In this paper, we propose a formal definition of a multi-argument function distance. The conventional definition of a distance is extended to apply to collections of more than two elements. Some general properties of multidistances are investigated and significant examples are exhibited. Finally, we introduce the concept of ball centered at a list in order to extend the one of the usual ball in...

Formal methods are seen as the Cinderella subject of software engineering, always hovering in the background, hoping to be invited to the ball. But exactly what are formal methods? Because they were fashionable in the eighties, the term was stolen by “informal” methods to provide themselves with a cloak of respectability-one of the claims of formal methods was that, by using them, it was possib...

In this note we consider a method of generating functions for systems with constraints and, as an example, we prove that the billiard mappings for billiards on the Euclidean space, sphere, and the Lobachevsky space are sympletic. Further, by taking a quadratic generating function we get the skew-hodograph mapping introduced by Moser and Veselov, which relates the ellipsoidal billiards in the Eu...

Abstract Domains and metric spaces are two central tools for the study of denotational semantics in computer science, but are otherwise very different in many fundamental aspects. A construction that tries to establish links between both paradigms is the space of formal balls, a continuous poset which can be defined for every metric space and that reflects many of its properties. On the other h...

We give en example-guided introduction to a framework that we have developed in recent years in order to extend the applicability of program verification to the context of systems modeled as infinite-state Markov chains. In particular, we describe the class of decisive Markov chains, and show how to perform qualitative and quantitative analysis of Markov chains that arise from probabilistic ext...

A model of the development of L0M cone ratios in the Old World primate retina is presented. It is supposed that during gestation, the cone cycles randomly between states in which it transcribes either L or M opsin. The current state determines and increases the probability that it will transcribe the same opsin in future cycles. These assumptions are sufficient to formalize the process as a Mar...

Electronic government invariably involves XML and electronic law: legislation is as essential to public administration as the ball is to a ball game. This paper gives an overview of two XML standard proposals dealing with two complementary aspects of electronic legislation – the documents themselves as a carrier, and an institutional reality they represent – in a coherent way: MetaLex XML and t...