research-article

Full Abstraction for Signal Flow Graphs

Authors:

Filippo Bonchi,

Pawel Sobocinski,

Fabio ZanasiAuthors Info & Claims

ACM SIGPLAN Notices, Volume 50, Issue 1

Pages 515 - 526

https://doi.org/10.1145/2775051.2676993

Published: 14 January 2015 Publication History

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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Cited By

Lindenhovius BMislove MZamdzhiev V(2023)Semantics for a Lambda Calculus for String DiagramsSamson Abramsky on Logic and Structure in Computer Science and Beyond10.1007/978-3-031-24117-8_26(973-1003)Online publication date: 2-Aug-2023
https://doi.org/10.1007/978-3-031-24117-8_26
Di Lavore Ede Felice GRomán M(2022)Monoidal Streams for Dataflow ProgrammingProceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3531130.3533365(1-14)Online publication date: 2-Aug-2022
https://dl.acm.org/doi/10.1145/3531130.3533365
Paixão JRufino LSobociński P(2022)High-level axioms for graphical linear algebraScience of Computer Programming10.1016/j.scico.2022.102791218(102791)Online publication date: Jun-2022
https://doi.org/10.1016/j.scico.2022.102791
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Index Terms

Full Abstraction for Signal Flow Graphs
1. Theory of computation
  1. Formal languages and automata theory
    1. Formalisms
      1. Algebraic language theory
  2. Semantics and reasoning
    1. Program semantics

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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
University of Kansas, Lawrence, KS

Issue’s Table of Contents

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
General Chair:
Sriram Rajamani
Microsoft Research, India
,
Program Chair:
David Walker
Princeton University, USA

Copyright © 2015 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 14 January 2015

Published in SIGPLAN Volume 50, Issue 1

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Cited By

Lindenhovius BMislove MZamdzhiev V(2023)Semantics for a Lambda Calculus for String DiagramsSamson Abramsky on Logic and Structure in Computer Science and Beyond10.1007/978-3-031-24117-8_26(973-1003)Online publication date: 2-Aug-2023
https://doi.org/10.1007/978-3-031-24117-8_26
Di Lavore Ede Felice GRomán M(2022)Monoidal Streams for Dataflow ProgrammingProceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3531130.3533365(1-14)Online publication date: 2-Aug-2022
https://dl.acm.org/doi/10.1145/3531130.3533365
Paixão JRufino LSobociński P(2022)High-level axioms for graphical linear algebraScience of Computer Programming10.1016/j.scico.2022.102791218(102791)Online publication date: Jun-2022
https://doi.org/10.1016/j.scico.2022.102791
Bonchi FPiedeleu RSobociński PZanasi F(2021)Bialgebraic foundations for the operational semantics of string diagramsInformation and Computation10.1016/j.ic.2021.104767(104767)Online publication date: May-2021
https://doi.org/10.1016/j.ic.2021.104767
Paixão JSobociński P(2020)Calculational Proofs in Relational Graphical Linear AlgebraFormal Methods: Foundations and Applications10.1007/978-3-030-63882-5_6(83-100)Online publication date: 19-Nov-2020
https://doi.org/10.1007/978-3-030-63882-5_6
Proença JCledou G(2020)ARx: Reactive Programming for Synchronous ConnectorsCoordination Models and Languages10.1007/978-3-030-50029-0_3(39-56)Online publication date: 10-Jun-2020
https://doi.org/10.1007/978-3-030-50029-0_3
Bonchi FPiedeleu RSobociński PZanasi FBouyer P(2019)Graphical affine algebraProceedings of the 34th Annual ACM/IEEE Symposium on Logic in Computer Science10.5555/3470152.3470211(1-12)Online publication date: 24-Jun-2019
https://dl.acm.org/doi/10.5555/3470152.3470211
Sprunger DKatsumata SBouyer P(2019)Differentiable causal computations via delayed traceProceedings of the 34th Annual ACM/IEEE Symposium on Logic in Computer Science10.5555/3470152.3470168(1-12)Online publication date: 24-Jun-2019
https://dl.acm.org/doi/10.5555/3470152.3470168
Sokolov APershin A(2019)Graph-Based Software Framework for Implementation of Complex Computational MethodsProgramming and Computing Software10.1134/S036176881905006245:5(257-267)Online publication date: 1-Sep-2019
https://dl.acm.org/doi/10.1134/S0361768819050062
Coecke BGenovese FLewis MMarsden DToumi A(2018)Generalized relations in linguistics & cognitionTheoretical Computer Science10.1016/j.tcs.2018.03.008752(104-115)Online publication date: Dec-2018
https://doi.org/10.1016/j.tcs.2018.03.008
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