The ``Synchronous The ``Synchronous Painter Painter Joaqun Joaqun - - PowerPoint PPT Presentation

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The ``Synchronous The ``Synchronous Painter Painter Joaqun Joaqun - - PowerPoint PPT Presentation

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The ``Synchronous The ``Synchronous Painter Painter Joaqun Joaqun Aguado guado University of Bamberg 3-Dec-2008 SYNCHRON08 . Idea Idea Rephrase causality analysis as a Graph Colouring Problem. Explain the step responses of

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3-Dec-2008 SYNCHRON‘08.

The ``Synchronous´´ The ``Synchronous´´ Painter Painter

Joaquín Joaquín Aguado guado

University of Bamberg

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Idea Idea

Rephrase causality analysis as a Graph Colouring Problem. Explain the step responses of Statecharts in terms of colourings.

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Graph Colouring Graph Colouring

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Graph Colouring Graph Colouring

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Graph Colouring Graph Colouring

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  • flat conjunction of

transitions

  • obtained from visual

syntax, structurally and incrementally

  • negations code non-

determinism, priorities and hierarchy

A-mazing A-mazing Components Components

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A-mazing A-mazing Components Components

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Words in Colour Words in Colour

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Colour Colour Patterns Patterns

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Model-Word Class Model-Word Class

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Concretising Concretising Colouring-Schemas Colouring-Schemas

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Classical Colouring Classical Colouring

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Classical Colouring Classical Colouring

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Pnueli Pnueli & Shalev & Shalev Statecharts tatecharts

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Pnueli Pnueli & Shalev & Shalev Statecharts tatecharts

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Pnueli Pnueli & Shalev & Shalev Statecharts tatecharts

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Pnueli Pnueli & Shalev & Shalev Statecharts tatecharts

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Pnueli Pnueli & Shalev & Shalev Statecharts tatecharts

Backtrack

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Pnueli Pnueli & Shalev & Shalev Statecharts tatecharts

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Pnueli Pnueli & Shalev & Shalev Statecharts tatecharts

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Pnueli Pnueli & Shalev & Shalev Statecharts tatecharts

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Intuitionistic Intuitionistic Colouring Colouring

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Intuitionistic Intuitionistic Colouring Colouring

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Intuitionistic Intuitionistic Colouring Colouring

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Intuitionistic Intuitionistic Colouring Colouring

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Intuitionistic Intuitionistic Colouring Colouring

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Intuitionistic Intuitionistic Colouring Colouring

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Intuitionistic Intuitionistic Colouring Colouring

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Intuitionistic Intuitionistic Colouring Colouring

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Intuitionistic Intuitionistic Colouring Colouring

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Intuitionistic Intuitionistic Colouring Colouring

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Intuitionistic Intuitionistic Colouring Colouring

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Intuitionistic Intuitionistic Colouring Colouring

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Summary Summary

This Colouring semantics corresponds to the macro-step semantics of Pnueli & Shalev. Graph colouring has concentrated on the optimisation (in the sense of minimality) under the proper colouring condition (i.e., there are no neighbours with the same colour) that despite all the efforts remains a very difficult combinatorial problem.

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Summary Summary

What our semantics is an immediate domain of application for graph colouring algorithms with weaker colouring conditions. Practical application will include, for example, semantic-based program transformations.

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Summary Summary

On the other hand, every algorithm implementing the synchronous semantics discussed here is automatically one colouring algorithm complying specific constraints. Also, not having considered other synchronous language we must leave

  • pen questions regarding the

possibility of extend our framework in particular to ESTEREL.