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Chu spaces and their interpretation as concurrent objects

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Computer Science Today

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1000))

Abstract

A Chu space is a binary relation

from a set A to an antiset X defined as a set which transforms via converse functions. Chu spaces admit a great many interpretations by virtue of realizing all small concrete categories and most large ones arising in mathematical and computational practice. Of particular interest for computer science is their interpretation as computational processes, which takes A to be a schedule of events distributed in time, X to be an automaton of states forming an information system in the sense of Scott, and the pairs (a, x) in the

relation to be the individual transcriptions of the making of history. The traditional homogeneous binary relations of transition on X and precedence on A are recovered as respectively the right and left residuals of the heterogeneous binary relation

with itself. The natural algebra of Chu spaces is that of linear logic, made a process algebra by the process interpretation.

This work was supported by ONR under grant number N00014-92-J-1974.

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Authors and Affiliations

  1. Dept. of Computer Science, Stanford University, 94305-2140, Stanford, CA

    Vaughan Pratt

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  1. Vaughan Pratt
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Jan van Leeuwen

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© 1995 Springer-Verlag Berlin Heidelberg

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Pratt, V. (1995). Chu spaces and their interpretation as concurrent objects. In: van Leeuwen, J. (eds) Computer Science Today. Lecture Notes in Computer Science, vol 1000. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015256

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  • DOI: https://doi.org/10.1007/BFb0015256

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  • Print ISBN: 978-3-540-60105-0

  • Online ISBN: 978-3-540-49435-5

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