The timed-based automata model, introduced by Alur and Dill, provides a useful formalism for describing real-time systems. Over the last two decades, several dense-time model checking tools have been developed based on that model. The paper considers the verification of real-time distributed commit protocols using dense-time model checking technology. More precisely, we model and verify the well-known timed two phase commit protocol in three different state-of-the-art real-time model checkers: UPPAAL, Rabbit, and RED, and compare the results.
The literature of timed automata theory is a rich literature since it was introduced by Alur and Dill in 1990. Alur and Madhusudan @cite_21 present a full survey of known results for decidability problems in timed automata theory. Tripakis @cite_13 gives algorithms and techniques to verify timed systems using TCTL logic and Timed Buchi Automata, which have implemented in KRONOS model checking tool. One of the disadvantages of KRONOS is that its input language supports a very restricted data types that allow only the declaration of clock variables. For this reason we have not included KRONOS in our comparative study.
@cite_21 @cite_13
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During the past few years, a number of verification tools have been developed for real-time systems in the framework of timed automata (e.g. KRONOS and UPPAAL). One of the major problems in applying these tools to industrial-size systems is the huge memory-usage for the exploration of the state-space of a network (or product) of timed automata, as the model-checkers must keep information on not only the control structure of the automata but also the clock values specified by clock constraints. In this paper, we present a compact data structure for representing clock constraints. The data structure is based on an O(n sup 3 ) algorithm which, given a constraint system over real-valued variables consisting of bounds on differences, constructs an equivalent system with a minimal number of constraints. In addition, we have developed an on-the-fly, reduction technique to minimize the space-usage. Based on static analysis of the control structure of a network of timed automata, we are able to compute a set of symbolic states that cover all the dynamic loops of the network in an on-the-fly searching algorithm, and thus ensure termination in reachability analysis. The two techniques and their combination have been implemented in the tool UPPAAL. Our experimental results demonstrate that the techniques result in truly significant space-reductions: for six examples from the literature, the space saving is between 75 and 94 , and in (nearly) all examples time-performance is improved. Also noteworthy is the observation that the two techniques are completely orthogonal. We investigate extensions of Alur and Dill's timed automata, based on the possibility to update the clocks in a more elaborate way than simply reset them to zero. We call these automata updatable timed automata. They form an undecidable class of models, in the sense that emptiness checking is not decidable. However, using an extension of the region graph construction, we exhibit interesting decidable subclasses. In a surprising way, decidability depends on the nature of the clock constraints which are used, diagonal-free or not, whereas these constraints play identical roles in timed automata. We thus describe in a quite precise way the thin frontier between decidable and undecidable classes of updatable timed automata.We also study the expressive power of updatable timed automata. It turns out that any up-datable automaton belonging to some decidable subclass can be effectively transformed into an equivalent timed automaton without updates but with silent transitions. The transformation suffers from an enormous combinatorics blow-up which seems unavoidable. Therefore, updatable timed automata appear to be a concise model for representing and analyzing large classes of timed systems. Alur, R. and D.L. Dill, A theory of timed automata, Theoretical Computer Science 126 (1994) 183-235. We propose timed (j&e) automata to model the behavior of real-time systems over time. Our definition provides a simple, and yet powerful, way to annotate state-transition graphs with timing constraints using finitely many real-valued clocks. A timed automaton accepts timed words-infinite sequences in which a real-valued time of occurrence is associated with each symbol. We study timed automata from the perspective of formal language theory: we consider closure properties, decision problems, and subclasses. We consider both nondeterministic and deterministic transition structures, and both Biichi and Muller acceptance conditions. We show that nondeterministic timed automata are closed under union and intersection, but not under complementation, whereas deterministic timed Muller automata are closed under all Boolean operations. The main construction of the paper is an (PSPACE) algorithm for checking the emptiness of the language of a (nondeterministic) timed automaton. We also prove that the universality problem and the language inclusion problem are solvable only for the deterministic automata: both problems are undecidable (II i-hard) in the nondeterministic case and PSPACE-complete in the deterministic case. Finally, we discuss the application of this theory to automatic verification of real-time requirements of finite-state systems. A monadic second-order language, denoted by ( L d ), is introduced for the specification of sets of timed state sequences. A fragment of ( L d ), denoted by , is proved to be expressively complete for timed automata (Alur and Dill), i.e., every timed regular language is definable by a -formula and every -formula defines a timed regular language. As a consequence the satisfiability problem for is decidable.