Event clock message passing automata: a logical characterization and an emptiness checking algorithm

  • Authors:

  • S. Akshay;Benedikt Bollig;Paul Gastin

  • Affiliations:

  • Laboratoire de Specification et Verification, ENS Cachan and CNRS, Cachan Cedex, France 94235;Laboratoire de Specification et Verification, ENS Cachan and CNRS, Cachan Cedex, France 94235;Laboratoire de Specification et Verification, ENS Cachan and CNRS, Cachan Cedex, France 94235

  • Venue:
  • Formal Methods in System Design
  • Year:
  • 2013

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Abstract

We are interested in modeling behaviors and verifying properties of systems in which time and concurrency play a crucial role. We introduce a model of distributed automata which are equipped with event clocks as in Alur et al. (Theor Comput Sci 211:253---273, 1999), which we call Event Clock Message Passing Automata (ECMPA). To describe the behaviors of such systems we use timed partial orders (modeled as message sequence charts with timing).Our first goal is to extend the classical Büchi-Elgot-Trakhtenbrot equivalence to the timed and distributed setting, by showing an equivalence between ECMPA and a timed extension of monadic second-order (MSO) logic. We obtain such a constructive equivalence in two different ways: (1) by restricting the semantics by bounding the set of timed partial orders; (2) by restricting the timed MSO logic to its existential fragment. We next consider the emptiness problem for ECMPA, which asks if a given ECMPA has some valid timed execution. In general this problem is undecidable and we show that by considering only bounded timed executions, we can obtain decidability. We do this by constructing a timed automaton which accepts all bounded timed executions of the ECMPA and checking emptiness of this timed automaton.