Document Open Access Logo

A Non-Standard Semantics for Kahn Networks in Continuous Time

Authors Romain Beauxis, Samuel Mimram



PDF
Thumbnail PDF

File

LIPIcs.CSL.2011.35.pdf
  • Filesize: 492 kB
  • 16 pages

Document Identifiers

Author Details

Romain Beauxis
Samuel Mimram

Cite AsGet BibTex

Romain Beauxis and Samuel Mimram. A Non-Standard Semantics for Kahn Networks in Continuous Time. In Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 12, pp. 35-50, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2011)
https://doi.org/10.4230/LIPIcs.CSL.2011.35

Abstract

In a seminal article, Kahn has introduced the notion of process network and given a semantics for those using Scott domains whose elements are (possibly infinite) sequences of values. This model has since then become a standard tool for studying distributed asynchronous computations. From the beginning, process networks have been drawn as particular graphs, but this syntax is never formalized. We take the opportunity to clarify it by giving a precise definition of these graphs, that we call nets. The resulting category is shown to be a fixpoint category, i.e. a cartesian category which is traced wrt the monoidal structure given by the product, and interestingly this structure characterizes the category: we show that it is the free fixpoint category containing a given set of morphisms, thus providing a complete axiomatics that models of process networks should satisfy. We then use these tools to build a model of networks in which data vary over a continuous time, in order to elaborate on the idea that process networks should also be able to encompass computational models such as hybrid systems or electric circuits. We relate this model to Kahn's semantics by introducing a third model of networks based on non-standard analysis, whose elements form an internal complete partial order for which many properties of standard domains can be reformulated. The use of hyperreals in this model allows it to formally consider the notion of infinitesimal, and thus to make a bridge between discrete and continuous time: time is "discrete", but the duration between two instants is infinitesimal. Finally, we give some examples of uses of the model by describing some networks implementing common constructions in analysis.
Keywords
  • Kahn network
  • non-standard analysis
  • fixpoint category
  • internal cpo

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail