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Dealing with practical limitations of distributed timed model checking for timed automata

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Abstract

Two base algorithms are known for reachability verification over timed automata. They are called forward and backwards, and traverse the automata edges using either successors or predecessors. Both usually work with a data structure called Difference Bound Matrices (DBMs). Although forward is better suited for on-the-fly construction of the model, the one known as backwards provides the basis for the verification of arbitrary formulae of the TCTL logic, and more importantly, for controller synthesis. Zeus is a distributed model checker for timed automata that uses the backwards algorithm. It works assigning each automata location to only one processor. This design choice seems the only reasonable way to deal with some complex operations involving many DBMs in order to avoid huge overheads due to distribution. This article explores the limitations of Zeus-like approaches for the distribution of timed model checkers.

Our findings justify why close-to-linear speedups are so difficult –and sometimes impossible– to achieve in the general case. Nevertheless, we present mechanisms based on the way model checking is usually applied. Among others, these include model-topology-aware partitioning and on-the-fly workload redistribution. Combined, they have a positive impact on the speedups obtained.

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Notes

  1. Not to be confused with the region graph presented in [6].

  2. A formal description of the architecture including state machines and transducers can be found in [32].

  3. Unluckily \(\tt{ParM{E}T{I}S}\) does not handle disconnected graphs, so the trick of disregarding the edges can't be used.

  4. In this type of observers, reachability of a distinguished location implies the existence of a run of the SUA that matches a given event scenario and hence violates some safety property.

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Authors and Affiliations

  1. Departamento de Computación, FCEyN, Universidad de Buenos Aires, Buenos Aires, Argentina

    V. Braberman & F. Schapachnik

  2. Centro de Estudios Avanzados, FIyCE, Universidad Argentina de la Empresa, Buenos Aires, Argentina

    A. Olivero

Authors
  1. V. Braberman
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  2. A. Olivero
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  3. F. Schapachnik
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Correspondence to V. Braberman.

Additional information

This research paper supported by BID OC/AR PICT 11738 grant.

V. Braberman: Research supported by UBACyT 2004 X020.

A. Olivero: Partially supported by UADE projects TSI04B and PI0509.

F. Schapachnik: Partially supported by an IDS 2003 grant.

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Braberman, V., Olivero, A. & Schapachnik, F. Dealing with practical limitations of distributed timed model checking for timed automata. Form Method Syst Des 29, 197–214 (2006). https://doi.org/10.1007/s10703-006-0012-3

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