In this paper, we show how the framework of von Neumann algebras can be applied to model the dynamics of computational processes. Namely, our aim is to gain an understanding of classical computation in terms of the hyperfinite II1 factor, starting from the class of Kalmar recursive functions. Our model fits within a vast pro ject of reshaping the unified theory of semantics of computation called geometry of interaction along the lines recently sketched by J.-Y. Girard.
An application of von Neumann Algebras to computational complexity
PIAZZA, Mario;
2010
Abstract
In this paper, we show how the framework of von Neumann algebras can be applied to model the dynamics of computational processes. Namely, our aim is to gain an understanding of classical computation in terms of the hyperfinite II1 factor, starting from the class of Kalmar recursive functions. Our model fits within a vast pro ject of reshaping the unified theory of semantics of computation called geometry of interaction along the lines recently sketched by J.-Y. Girard.File in questo prodotto:
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