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On characteristic formulae for Event-Recording Automata∗

Published online by Cambridge University Press:  10 January 2013

Omer Landry Nguena Timo  and
Pierre-Alain Reynier
Omer Landry Nguena Timo
Affiliation:
Laboratoire Bordelais de Recherche en Informatique (LaBRI), Université Bordeaux 1, 351 cours de la Libération, 33405 Talence Cedex, France.. [email protected]
Pierre-Alain Reynier
Affiliation:
Laboratoire d’Informatique Fondamentale (LIF), Aix-Marseille Université, 39 avenue Joliot-Curie, 13453 Marseille Cedex 13, France.; [email protected]
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Abstract

A standard bridge between automata theory and logic is provided by the notion ofcharacteristic formula. This paper investigates this problem for the class ofevent-recording automata (ERA), a subclass of timed automata in which clocks areassociated with actions and that enjoys very good closure properties. We first study theproblem of expressing characteristic formulae for ERA in Event-Recording Logic (ERL ), alogic introduced by Sorea to express event-based timed specifications. We prove that theconstruction proposed by Sorea for ERA without invariants is incorrect. More generally, weprove that timed bisimilarity cannot in general be expressed in ERL for the class of ERA ,and study under which conditions on ERA it can be. Then, we introduce the logicWTμ , a new logic for event-based timed specificationscloser to the timed logic ℒν that was introduced byLaroussinie, Larsen and Weise. We prove that it is strictly more expressive than ERL , andthat its model-checking problem against ERA is EXPTIME -complete. Finally, we providecharacteristic formulae constructions in WTμ forcharacterizing the general class of ERA up to timed (bi)similarity and study thecomplexity issues.

Keywords

Timed Logicbisimulationevent-clock automata
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 47 , Issue 1 , January 2013 , pp. 69 - 96
Copyright
© EDP Sciences 2013

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