A Unified Model for Real-Time Systems: Symbolic Techniques and Implementation

In this paper, we consider a model of generalized timed automata (GTA) with two kinds of clocks, history and future, that can express many timed features succinctly, including timed automata, event-clock automata with and without diagonal constraints, and automata with timers. Our main contribution is a new simulation-based zone algorithm for checking reachability in this unified model. While such algorithms are known to exist for timed automata, and have recently been shown for event-clock automata without diagonal constraints, this is the first result that can handle event-clock automata with diagonal constraints and automata with timers. We also provide a prototype implementation for our model and show experimental results on several benchmarks. To the best of our knowledge, this is the first effective implementation not just for our unified model, but even just for automata with timers or for event-clock automata (with predicting clocks) without going through a costly translation via timed automata. Last but not least, beyond being interesting in their own right, generalized timed automata can be used for model-checking event-clock specifications over timed automata models

Reachability in Timed Automata with Diagonal Constraints

We consider the reachability problem for timed automata having diagonal constraints (like x - y < 5) as guards in transitions. The best algorithms for timed automata proceed by enumerating reachable sets of its configurations, stored in a data structure called "zones". Simulation relations between zones are essential to ensure termination and efficiency. The algorithm employs a simulation test Z <= Z\u27 which ascertains that zone Z does not reach more states than zone Z\u27, and hence further enumeration from Z is not necessary. No effective simulations are known for timed automata containing diagonal constraints as guards. We propose a simulation relation <=_{LU}^d for timed automata with diagonal constraints. On the negative side, we show that deciding Z not <=_{LU}^d Z\u27 is NP-complete. On the positive side, we identify a witness for Z not <=_{LU}^d Z\u27 and propose an algorithm to decide the existence of such a witness using an SMT solver. The shape of the witness reveals that the simulation test is likely to be efficient in practice

Zone-based verification of timed automata: extrapolations, simulations and what next?

Timed automata have been introduced by Rajeev Alur and David Dill in the early 90's. In the last decades, timed automata have become the de facto model for the verification of real-time systems. Algorithms for timed automata are based on the traversal of their state-space using zones as a symbolic representation. Since the state-space is infinite, termination relies on finite abstractions that yield a finite representation of the reachable states. The first solution to get finite abstractions was based on extrapolations of zones, and has been implemented in the industry-strength tool Uppaal. A different approach based on simulations between zones has emerged in the last ten years, and has been implemented in the fully open source tool TChecker. The simulation-based approach has led to new efficient algorithms for reachability and liveness in timed automata, and has also been extended to richer models like weighted timed automata, and timed automata with diagonal constraints and updates. In this article, we survey the extrapolation and simulation techniques, and discuss some open challenges for the future.Comment: Invited contribution at FORMATS'2

Timed pushdown automata revisited

This paper contains two results on timed extensions of pushdown automata (PDA). As our first result we prove that the model of dense-timed PDA of Abdulla et al. collapses: it is expressively equivalent to dense-timed PDA with timeless stack. Motivated by this result, we advocate the framework of first-order definable PDA, a specialization of PDA in sets with atoms, as the right setting to define and investigate timed extensions of PDA. The general model obtained in this way is Turing complete. As our second result we prove NEXPTIME upper complexity bound for the non-emptiness problem for an expressive subclass. As a byproduct, we obtain a tight EXPTIME complexity bound for a more restrictive subclass of PDA with timeless stack, thus subsuming the complexity bound known for dense-timed PDA.Comment: full technical report of LICS'15 pape

Quantitative model checking of continuous-time Markov chains against timed automata specifications

We study the following problem: given a continuous-time Markov chain (CTMC) C, and a linear real-time property provided as a deterministic timed automaton (DTA) A, what is the probability of the set of paths of C that are\ud accepted by A (C satisfies A)? It is shown that this set of paths is measurable and computing its probability can be reduced to computing the reachability probability in a piecewise deterministic Markov process (PDP). The reachability probability is characterized as the least solution of a system of integral equations and is shown to be approximated by solving a system of partial differential equations. For the special case of single-clock DTA, the system of integral equations can be transformed into a system of linear equations where the coefficients are solutions of ordinary differential equations

Better abstractions for timed automata

We consider the reachability problem for timed automata. A standard solution to this problem involves computing a search tree whose nodes are abstractions of zones. These abstractions preserve underlying simulation relations on the state space of the automaton. For both effectiveness and efficiency reasons, they are parametrized by the maximal lower and upper bounds (LU-bounds) occurring in the guards of the automaton. We consider the aLU abstraction defined by Behrmann et al. Since this abstraction can potentially yield non-convex sets, it has not been used in implementations. We prove that aLU abstraction is the biggest abstraction with respect to LU-bounds that is sound and complete for reachability. We also provide an efficient technique to use the aLU abstraction to solve the reachability problem.Comment: Extended version of LICS 2012 paper (conference paper till v6). in Information and Computation, available online 27 July 201

Polynomial Interrupt Timed Automata

Interrupt Timed Automata (ITA) form a subclass of stopwatch automata where reachability and some variants of timed model checking are decidable even in presence of parameters. They are well suited to model and analyze real-time operating systems. Here we extend ITA with polynomial guards and updates, leading to the class of polynomial ITA (PolITA). We prove the decidability of the reachability and model checking of a timed version of CTL by an adaptation of the cylindrical decomposition method for the first-order theory of reals. Compared to previous approaches, our procedure handles parameters and clocks in a unified way. Moreover, we show that PolITA are incomparable with stopwatch automata. Finally additional features are introduced while preserving decidability