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Full Abstraction for Signal Flow Graphs

Published:14 January 2015Publication History
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Abstract

Network theory uses the string diagrammatic language of monoidal categories to study graphical structures formally, eschewing specialised translations into intermediate formalisms. Recently, there has been a concerted research focus on developing a network theoretic approach to signal flow graphs, which are classical structures in control theory, signal processing and a cornerstone in the study of feedback. In this approach, signal flow graphs are given a relational denotational semantics in terms of formal power series.

Thus far, the operational behaviour of such signal flow graphs has only been discussed at an intuitive level. In this paper we equip them with a structural operational semantics. As is typically the case, the purely operational picture is too concrete -- two graphs that are denotationally equal may exhibit different operational behaviour. We classify the ways in which this can occur and show that any graph can be realised -- rewritten, using the graphical theory, into an executable form where the operational behavior and the denotation coincides.

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          • Published in

            cover image ACM SIGPLAN Notices
            ACM SIGPLAN Notices  Volume 50, Issue 1
            POPL '15
            January 2015
            682 pages
            ISSN:0362-1340
            EISSN:1558-1160
            DOI:10.1145/2775051
            • Editor:
            • Andy Gill
            Issue’s Table of Contents
            • cover image ACM Conferences
              POPL '15: Proceedings of the 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
              January 2015
              716 pages
              ISBN:9781450333009
              DOI:10.1145/2676726

            Copyright © 2015 ACM

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            Association for Computing Machinery

            New York, NY, United States

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            • Published: 14 January 2015

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