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A Categorical Semantics of Signal Flow Graphs

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CONCUR 2014 – Concurrency Theory (CONCUR 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8704))

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Abstract

We introduce \(\mathbb{IH}\), a sound and complete graphical theory of vector subspaces over the field of polynomial fractions, with relational composition. The theory is constructed in modular fashion, using Lack’s approach to composing PROPs with distributive laws.

We then view string diagrams of \(\mathbb{IH}\) as generalised stream circuits by using a formal Laurent series semantics. We characterize the subtheory where circuits adhere to the classical notion of signal flow graphs, and illustrate the use of the graphical calculus on several examples.

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Authors and Affiliations

  1. ENS de Lyon, Université de Lyon, CNRS, INRIA, France

    Filippo Bonchi & Fabio Zanasi

  2. ECS, University of Southampton, UK

    Paweł Sobociński

Authors
  1. Filippo Bonchi
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  2. Paweł Sobociński
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  3. Fabio Zanasi
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Padova, Via Trieste, 63, 35121, Padova, Italy

    Paolo Baldan

  2. Department of Computer Science, University of Roma “La Sapienza”, Via Salaria, 113, 00198, Rome, Italy

    Daniele Gorla

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Bonchi, F., Sobociński, P., Zanasi, F. (2014). A Categorical Semantics of Signal Flow Graphs. In: Baldan, P., Gorla, D. (eds) CONCUR 2014 – Concurrency Theory. CONCUR 2014. Lecture Notes in Computer Science, vol 8704. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44584-6_30

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  • DOI: https://doi.org/10.1007/978-3-662-44584-6_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44583-9

  • Online ISBN: 978-3-662-44584-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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