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Full abstraction for signal flow graphs

Full abstraction for signal flow graphs
Full abstraction for signal flow graphs


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.
515-526
Sobocinski, Pawel
439334ab-2826-447b-9fe5-3928be3fd4fd
Sobocinski, Pawel
439334ab-2826-447b-9fe5-3928be3fd4fd

Sobocinski, Pawel (2015) Full abstraction for signal flow graphs At POPL '15: Proceedings of the 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, India. 12 - 18 Jan 2015. , pp. 515-526.

Record type: Conference or Workshop Item (Paper)

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 date: 14 January 2015
Venue - Dates: POPL '15: Proceedings of the 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, India, 2015-01-12 - 2015-01-18
Organisations: Electronic & Software Systems

Identifiers

Local EPrints ID: 396535
URI: https://eprints.soton.ac.uk/id/eprint/396535
PURE UUID: 2d47fd9f-d280-4b6c-b6a6-7ffc9804291e

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Date deposited: 08 Jun 2016 15:52
Last modified: 25 Oct 2017 22:17

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Contributors

Author: Pawel Sobocinski

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