A Categorical Semantics of Signal Flow Graphs

  • Filippo Bonchi
  • Paweł Sobociński
  • Fabio Zanasi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8704)


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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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Filippo Bonchi
    • 1
  • Paweł Sobociński
    • 2
  • Fabio Zanasi
    • 1
  1. 1.ENS de LyonUniversité de Lyon, CNRS, INRIAFrance
  2. 2.ECSUniversity of SouthamptonUK

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