research-article

Full Abstraction for Signal Flow Graphs

Authors:

Filippo Bonchi,

Pawel Sobocinski,

Fabio ZanasiAuthors Info & Claims

POPL '15: Proceedings of the 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

Pages 515 - 526

https://doi.org/10.1145/2676726.2676993

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

Bonchi FDi Giorgio AHaydon NSobocinski PSobocinski PLago UEsparza J(2024)Diagrammatic Algebra of First Order LogicProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662078(1-15)Online publication date: 8-Jul-2024
https://dl.acm.org/doi/10.1145/3661814.3662078
Bonchi FDi Giorgio ASantamaria A(2023)Deconstructing the Calculus of Relations with Tape DiagramsProceedings of the ACM on Programming Languages10.1145/35712577:POPL(1864-1894)Online publication date: 11-Jan-2023
https://dl.acm.org/doi/10.1145/3571257
Bonchi FGadducci FKissinger ASobocinski PZanasi F(2022)String Diagram Rewrite Theory I: Rewriting with Frobenius StructureJournal of the ACM10.1145/350271969:2(1-58)Online publication date: 10-Mar-2022
https://dl.acm.org/doi/10.1145/3502719
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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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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

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

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

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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SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

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New York, NY, United States

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Published: 14 January 2015

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Agence Nationale de la Recherche

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POPL '15

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SIGPLAN

POPL '15: The 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

January 15 - 17, 2015

Mumbai, India

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POPL '15 Paper Acceptance Rate 52 of 227 submissions, 23%;

Overall Acceptance Rate 824 of 4,130 submissions, 20%

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The 52nd Annual ACM SIGPLAN Symposium on Principles of Programming Languages

January 19 - 25, 2025

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Cited By

Bonchi FDi Giorgio AHaydon NSobocinski PSobocinski PLago UEsparza J(2024)Diagrammatic Algebra of First Order LogicProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662078(1-15)Online publication date: 8-Jul-2024
https://dl.acm.org/doi/10.1145/3661814.3662078
Bonchi FDi Giorgio ASantamaria A(2023)Deconstructing the Calculus of Relations with Tape DiagramsProceedings of the ACM on Programming Languages10.1145/35712577:POPL(1864-1894)Online publication date: 11-Jan-2023
https://dl.acm.org/doi/10.1145/3571257
Bonchi FGadducci FKissinger ASobocinski PZanasi F(2022)String Diagram Rewrite Theory I: Rewriting with Frobenius StructureJournal of the ACM10.1145/350271969:2(1-58)Online publication date: 10-Mar-2022
https://dl.acm.org/doi/10.1145/3502719
Bonchi FGadducci FKissinger ASobociński PZanasi F(2022)String diagram rewrite theory III: Confluence with and without FrobeniusMathematical Structures in Computer Science10.1017/S096012952200012332:7(829-869)Online publication date: 13-Jun-2022
https://doi.org/10.1017/S0960129522000123
Ghica D(2021)Operational Semantics with Hierarchical Abstract Syntax GraphsElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.334.1334(1-10)Online publication date: 8-Feb-2021
https://doi.org/10.4204/EPTCS.334.1
Bonchi FSobociński PZanasi F(2021)A Survey of Compositional Signal Flow TheoryAdvancing Research in Information and Communication Technology10.1007/978-3-030-81701-5_2(29-56)Online publication date: 4-Aug-2021
https://doi.org/10.1007/978-3-030-81701-5_2
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 F(2020)Contextual Equivalence for Signal Flow GraphsFoundations of Software Science and Computation Structures10.1007/978-3-030-45231-5_5(77-96)Online publication date: 25-Apr-2020
https://dl.acm.org/doi/10.1007/978-3-030-45231-5_5
Zamdzhiev V(2019)A Framework for Rewriting Families of String DiagramsElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.288.6288(63-76)Online publication date: 6-Feb-2019
https://doi.org/10.4204/EPTCS.288.6
Bonchi FHolland JPiedeleu RSobociński PZanasi F(2019)Diagrammatic algebra: from linear to concurrent systemsProceedings of the ACM on Programming Languages10.1145/32903383:POPL(1-28)Online publication date: 2-Jan-2019
https://dl.acm.org/doi/10.1145/3290338
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