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Computability structures, simulations and realizability

Published online by Cambridge University Press:  05 June 2013

JOHN LONGLEY
JOHN LONGLEY*
Affiliation:
Laboratory for Foundations of Computer Science, School of Informatics, University of Edinburgh, 10 Crichton Street, Edinburgh, EH8 9AB, United Kingdom Email: jrl@staffmail.ed.ac.uk
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Abstract

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We generalise the standard construction of realizability models (specifically, of categories of assemblies) to a wide class of computability structures, which is broad enough to embrace models of computation such as labelled transition systems and process algebras. We consider a general notion of simulation between such computability structures, and show how these simulations correspond precisely to certain functors between the realizability models. Furthermore, we show that our class of computability structures has good closure properties – in particular, it is ‘cartesian closed’ in a slightly relaxed sense. Finally, we investigate some important subclasses of computability structures and of simulations between them. We suggest that our 2-category of computability structures and simulations may offer a useful framework for investigating questions of computational power, abstraction and simulability for a wide range of models.

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Type
Paper
Information
Mathematical Structures in Computer Science , Volume 24 , Issue 2 , April 2014 , e240201
Copyright
Copyright © Cambridge University Press 2013 

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