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On the Scott-continuity of tagged signal processes

Laurent Moss, Guy Bois

Technical Report (2009)

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Résumé

Process networks are frequently used to model signal processing and multimediaapplications. It is important to ensure that a process network hasa uniquely defined behavior in order to correctly model such deterministicsystems. Furthermore, a constructive procedure to determine this uniquebehavior is necessary for its simulation and execution.By the Kahn principle, the unique behavior of a process network is knownto be the least fixed point of the network functional when every processcomputes a Scott-continuous function. The Kahn principle is used in arecent timed extension of the least fixed point semantics of Kahn processnetworks, using the tagged signal model. In this extension, processes computea function from input signals to output signals, where a signal is defined as apartial function from a down set of tags to a set of values. However, it is oftentedious to formally prove that a tagged signal process is Scott-continuous.This paper presents theorems on Scott-continuity that simplify such proofs.Thus, a general theorem on the necessary and sufficient conditions for theScott-continuity of tagged signal processes is proven. Scott-continuity is thenproven for broad classes of processes, namely the classes of exactly causalprocesses and of domain-warping processes, which include stateless processes,delays as well as a subset of discrete-event processes.

Uncontrolled Keywords

Process networks, Denotational semantics, Timed systems, Discrete events, Dataflow

Subjects: 2700 Information technology > 2700 Information technology
2700 Information technology > 2719 Computer architecture and design
Department: Department of Computer Engineering and Software Engineering
PolyPublie URL: https://publications.polymtl.ca/2640/
Report number: EPM-RT-2009-01
Date Deposited: 06 Oct 2017 13:37
Last Modified: 09 Nov 2022 22:00
Cite in APA 7: Moss, L., & Bois, G. (2009). On the Scott-continuity of tagged signal processes (Technical Report n° EPM-RT-2009-01). https://publications.polymtl.ca/2640/

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