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Task 4/5.3 : Timing analysis

The methodology developed in task 4/5.2 also allows us to perform architecture profiling: having a model for a synchronous program running on a distributed architecture, we can replace each elementary process in this model, by another one, modelling time elapsing. This allows us to produce a program which simulates how much time is needed for the target architecture to execute. Such timing simulator can then be given to packages for subsequent analysis: is this or that particular real-time or timeliness property satisfied?

There are approaches along the lines of timed automata that can be considered. We have been looking instead in a different direction, namely the use of so-called MaxPlus algebra. In particular, MaxPlus automata have been introduced by this school as a way to model time consuming for machines having a finite set of different running modes. This is interesting as it provides us with techniques to evaluate infinite timing behaviours for our system (such as, e.g., steady-state throughput), something not available from competing approaches from temporal logic. And this holds, both for synchronous programs and their desynchronised execution, following the principles and method from tasks 4/5.1 and 4/5.2. Thus there is a need

  1. to develop in MaxPlus algebra the kind of algorithm needed to answer questions of interest to us,
  2. to have a link between synchronous languages or formalisms and MaxPlus algebra symbolic models.
As point 2 depends on the development of packages by the MaxPlus community (in particular within the framework of LTR project Alapedes) it is difficult to schedule the availability of software prototypes.
deliverable 4/5.3.2
(24 months). Showing the approach and the kind of property that can be expressed and reasoned about; having a first set of algorithms.
deliverable 4/5.3.3
(36 months). Connecting synchronous formalisms to MaxPlus formalisms: specification, and possibly light prototyping, depending on availability of appropriate software from the MaxPlus community. Having algorithms that can scale up to large systems. Application examples whenever possible.

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