Physical computation and compositionality

Developments in quantum computing and, more in general, non-standard computing systems, represent a clear indication that the very notion of what a physical computing device is and does should be recast in a rigorous and sound framework. Physical computing has opened a whole stream of new research aimed to understand and control how information is processed by several types of physical devices. Therefore, classical definitions and entire frameworks need to be adapted in order to fit a broader notion of what physical computing systems really are. Recent studies have proposed a formalism that can be used to carve out a more proper notion of physical computing. In this paper we present a framework which capture such results in a very natural way via some basic constructions in Category Theory. Furthermore, we show that, within our framework, the compositional nature of physical computing systems is naturally formalized, and that it can be organized in coherent structures by the means of their relational nature.

Notes on a model for fuzzy computing

In these notes we propose a setting for fuzzy computing in a framework similar to that of well-established theories of computation: boolean, and quantum computing. Our efforts have been directed towards stressing the formal similarities: there is a common pattern underlying these three theories. We tried to conform our approach, as much as possible, to this pattern. This work was part of a project jointly with Professor Vittorio Cafagna. Professor Cafagna passed away unexpectedly in 2007. His intellectual breadth and inspiring passion for mathematics is still very well alive.