research-article

Algebra of Parameterised Graphs

Authors:

Victor KhomenkoAuthors Info & Claims

ACM Transactions on Embedded Computing Systems (TECS), Volume 13, Issue 4s

Article No.: 143, Pages 1 - 22

https://doi.org/10.1145/2627351

Published: 28 July 2014 Publication History

Abstract

One of the difficulties in designing modern hardware systems is the necessity for comprehending and dealing with a very large number of system configurations, operational modes, and behavioural scenarios. It is often infeasible to consider and specify each individual mode explicitly, and one needs methodologies and tools to exploit similarities between the individual modes and work with groups of modes rather than individual ones. The modes and groups of modes have to be managed in a compositional way: the specification of the system should be composed from specifications of its blocks. This includes both structural and behavioural composition. Furthermore, one should be able to transform and optimise the specifications in a formal way.

In this article, we propose a new formalism, called parameterised graphs. It extends the existing conditional partial order graphs (CPOGs) formalism in several ways. First, it deals with general graphs rather than just partial orders. Moreover, it is fully compositional. To achieve this, we introduce an algebra of parameterised graphs by specifying the equivalence relation by a set of axioms, which is proved to be sound, minimal, and complete. This allows one to manipulate the specifications as algebraic expressions using the rules of this algebra. We demonstrate the usefulness of the developed formalism on several case studies coming from the area of microelectronics design.

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Cited By

de Gennaro ASokolov DMokhov A(2020)Design and Implementation of Reconfigurable Asynchronous PipelinesIEEE Transactions on Very Large Scale Integration (VLSI) Systems10.1109/TVLSI.2020.2975591(1-13)Online publication date: 2020
https://doi.org/10.1109/TVLSI.2020.2975591
Beaumont JMokhov ASokolov DYakovlev A(2018)High-Level Asynchronous Concepts at the Interface Between Analog and Digital WorldsIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems10.1109/TCAD.2017.274800237:1(61-74)Online publication date: Jan-2018
https://doi.org/10.1109/TCAD.2017.2748002
Ponce De León HMokhov A(2018)Compact and efficiently verifiable models for concurrent systemsFormal Methods in System Design10.1007/s10703-018-0316-053:3(407-431)Online publication date: 1-Dec-2018
https://dl.acm.org/doi/10.1007/s10703-018-0316-0
Show More Cited By

Index Terms

Algebra of Parameterised Graphs
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory

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Published In

cover image ACM Transactions on Embedded Computing Systems

ACM Transactions on Embedded Computing Systems Volume 13, Issue 4s

Special Issue on Real-Time and Embedded Technology and Applications, Domain-Specific Multicore Computing, Cross-Layer Dependable Embedded Systems, and Application of Concurrency to System Design (ACSD'13)

July 2014

571 pages

ISSN:1539-9087

EISSN:1558-3465

DOI:10.1145/2601432

Editors:
Sandeep K. Shukla
Virginia Tech, USA
,
Josep Carmona
Universitat Politècnica de Catalunya, Spain
,
Mihai Teodor Lazarescu
Politecnico di Torino, Italy
,
Marta Pietkiewicz-koutny
Newcastle University, UK

Issue’s Table of Contents

Copyright © 2014 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 the author(s) 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

Journal Family

ACM Journals for the Design of Smart and Connected Systems

Publication History

Published: 28 July 2014

Accepted: 01 February 2014

Received: 01 October 2013

Published in TECS Volume 13, Issue 4s

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Cited By

de Gennaro ASokolov DMokhov A(2020)Design and Implementation of Reconfigurable Asynchronous PipelinesIEEE Transactions on Very Large Scale Integration (VLSI) Systems10.1109/TVLSI.2020.2975591(1-13)Online publication date: 2020
https://doi.org/10.1109/TVLSI.2020.2975591
Beaumont JMokhov ASokolov DYakovlev A(2018)High-Level Asynchronous Concepts at the Interface Between Analog and Digital WorldsIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems10.1109/TCAD.2017.274800237:1(61-74)Online publication date: Jan-2018
https://doi.org/10.1109/TCAD.2017.2748002
Ponce De León HMokhov A(2018)Compact and efficiently verifiable models for concurrent systemsFormal Methods in System Design10.1007/s10703-018-0316-053:3(407-431)Online publication date: 1-Dec-2018
https://dl.acm.org/doi/10.1007/s10703-018-0316-0
Mokhov A(2017)Algebraic graphs with class (functional pearl)ACM SIGPLAN Notices10.1145/3156695.312295652:10(2-13)Online publication date: 7-Sep-2017
https://dl.acm.org/doi/10.1145/3156695.3122956
Cogumbreiro TSurendran RMartins FSarkar VVasconcelos VGrossman M(2017)Deadlock avoidance in parallel programs with futures: why parallel tasks should not wait for strangersProceedings of the ACM on Programming Languages10.1145/31433591:OOPSLA(1-26)Online publication date: 12-Oct-2017
https://dl.acm.org/doi/10.1145/3143359
Mokhov ADiatchki I(2017)Algebraic graphs with class (functional pearl)Proceedings of the 10th ACM SIGPLAN International Symposium on Haskell10.1145/3122955.3122956(2-13)Online publication date: 7-Sep-2017
https://dl.acm.org/doi/10.1145/3122955.3122956
Mokhov ACortadella Jde Gennaro A(2017)Process Windows2017 17th International Conference on Application of Concurrency to System Design (ACSD)10.1109/ACSD.2017.18(86-95)Online publication date: Jun-2017
https://doi.org/10.1109/ACSD.2017.18
Beaumont J(2017)Plato: A Tool for Behavioural Specification of Asynchronous Circuits2017 17th International Conference on Application of Concurrency to System Design (ACSD)10.1109/ACSD.2017.14(68-73)Online publication date: Jun-2017
https://doi.org/10.1109/ACSD.2017.14
Bhattacharyya AMokhov APierce K(2017)An empirical comparison of formalisms for modelling and analysis of dynamic reconfiguration of dependable systemsFormal Aspects of Computing10.1007/s00165-016-0405-z29:2(251-307)Online publication date: 1-Mar-2017
https://dl.acm.org/doi/10.1007/s00165-016-0405-z
Mokhov AMitchell NPeyton Jones SMarlow S(2016)Non-recursive make considered harmful: build systems at scaleACM SIGPLAN Notices10.1145/3241625.297601151:12(170-181)Online publication date: 8-Sep-2016
https://dl.acm.org/doi/10.1145/3241625.2976011
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