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A Brief Guide to Linear Logic
, 1993
"... An overview of linear logic is given, including an extensive bibliography and a simple example of the close relationship between linear logic and computation. ..."
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Cited by 53 (8 self)
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An overview of linear logic is given, including an extensive bibliography and a simple example of the close relationship between linear logic and computation.
Nuclear and Trace Ideals in Tensored *Categories
, 1998
"... We generalize the notion of nuclear maps from functional analysis by defining nuclear ideals in tensored categories. The motivation for this study came from attempts to generalize the structure of the category of relations to handle what might be called "probabilistic relations". The compact closed ..."
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Cited by 28 (10 self)
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We generalize the notion of nuclear maps from functional analysis by defining nuclear ideals in tensored categories. The motivation for this study came from attempts to generalize the structure of the category of relations to handle what might be called "probabilistic relations". The compact closed structure associated with the category of relations does not generalize directly, instead one obtains nuclear ideals. Most tensored categories have a large class of morphisms which behave as if they were part of a compact closed category, i.e. they allow one to transfer variables between the domain and the codomain. We introduce the notion of nuclear ideals to analyze these classes of morphisms. In compact closed tensored categories, all morphisms are nuclear, and in the tensored category of Hilbert spaces, the nuclear morphisms are the HilbertSchmidt maps. We also introduce two new examples of tensored categories, in which integration plays the role of composition. In the first, mor...
Dynamics of Algorithms
"... This paper represents an extended version of [16]. In the next section we describe partially additive categories. In section 3 we present the execution of pseudoalgorithms in the framework of the partially additive categories as a kind of iteration of endomorphisms. Moreover, we consider deadlock fr ..."
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This paper represents an extended version of [16]. In the next section we describe partially additive categories. In section 3 we present the execution of pseudoalgorithms in the framework of the partially additive categories as a kind of iteration of endomorphisms. Moreover, we consider deadlock free pseudoalgorithms as to be characterized by a summability condition; concepts about structural aspects are organized via type discipline and type compatible dynamics.