Gianluca Caterina

Nima Dehghani, Gianluca Caterina

This paper introduces a category theory-based framework to redefine physical computing in light of advancements in quantum computing and non-standard computing systems. By integrating classical definitions within this broader perspective, the paper rigorously recontextualizes what constitutes physical computing devices and processes. It demonstrates how the compositional nature and relational structures of physical computing systems can be coherently formalized using category theory. This approach not only encapsulates recent formalisms in physical computing but also offers a structured method to explore the dynamic interactions within these systems.

Vittorio Cafagna, Gianluca Caterina

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.