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

Testing real-time systems using TINA

The paper presents a technique for model-based black-box conformance testing of real-time systems using the Time Petri Net Analyzer TINA. Such test suites are derived from a prioritized time Petri net composed of two concurrent sub-nets specifying respectively the expected behaviour of the system under test and its environment.We describe how the toolbox TINA has been extended to support automatic generation of time-optimal test suites. The result is optimal in the sense that the set of test cases in the test suite have the shortest possible accumulated time to be executed. Input/output conformance serves as the notion of implementation correctness, essentially timed trace inclusion taking environment assumptions into account. Test cases selection is based either on using manually formulated test purposes or automatically from various coverage criteria specifying structural criteria of the model to be fulfilled by the test suite. We discuss how test purposes and coverage criterion are specified in the linear temporal logic SE-LTL, derive test sequences, and assign verdicts

Verification and Control of Partially Observable Probabilistic Real-Time Systems

We propose automated techniques for the verification and control of probabilistic real-time systems that are only partially observable. To formally model such systems, we define an extension of probabilistic timed automata in which local states are partially visible to an observer or controller. We give a probabilistic temporal logic that can express a range of quantitative properties of these models, relating to the probability of an event's occurrence or the expected value of a reward measure. We then propose techniques to either verify that such a property holds or to synthesise a controller for the model which makes it true. Our approach is based on an integer discretisation of the model's dense-time behaviour and a grid-based abstraction of the uncountable belief space induced by partial observability. The latter is necessarily approximate since the underlying problem is undecidable, however we show how both lower and upper bounds on numerical results can be generated. We illustrate the effectiveness of the approach by implementing it in the PRISM model checker and applying it to several case studies, from the domains of computer security and task scheduling

Tapered-amplified AR-coated laser diodes for Potassium and Rubidium atomic-physics experiments

We present a system of room-temperature extended-cavity grating-diode lasers (ECDL) for production of light in the range 760-790nm. The extension of the tuning range towards the blue is permitted by the weak feedback in the cavity: the diodes are anti-reflection coated, and the grating has just 10% reflectance. The light is then amplified using semiconductor tapered amplifiers to give more than 400mW of power. The outputs are shown to be suitable for atomic physics experiments with potassium (767nm), rubidium (780nm) or both, of particular relevance to doubly-degenerate boson-fermion mixtures

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

Efficient Emptiness Check for Timed B\"uchi Automata (Extended version)

The B\"uchi non-emptiness problem for timed automata refers to deciding if a given automaton has an infinite non-Zeno run satisfying the B\"uchi accepting condition. The standard solution to this problem involves adding an auxiliary clock to take care of the non-Zenoness. In this paper, it is shown that this simple transformation may sometimes result in an exponential blowup. A construction avoiding this blowup is proposed. It is also shown that in many cases, non-Zenoness can be ascertained without extra construction. An on-the-fly algorithm for the non-emptiness problem, using non-Zenoness construction only when required, is proposed. Experiments carried out with a prototype implementation of the algorithm are reported.Comment: Published in the Special Issue on Computer Aided Verification - CAV 2010; Formal Methods in System Design, 201

Anisotropic 2D diffusive expansion of ultra-cold atoms in a disordered potential

We study the horizontal expansion of vertically confined ultra-cold atoms in the presence of disorder. Vertical confinement allows us to realize a situation with a few coupled harmonic oscillator quantum states. The disordered potential is created by an optical speckle at an angle of 30{\deg} with respect to the horizontal plane, resulting in an effective anisotropy of the correlation lengths of a factor of 2 in that plane. We observe diffusion leading to non-Gaussian density profiles. Diffusion coefficients, extracted from the experimental results, show anisotropy and strong energy dependence, in agreement with numerical calculations

Interrupt Timed Automata: verification and expressiveness

We introduce the class of Interrupt Timed Automata (ITA), a subclass of hybrid automata well suited to the description of timed multi-task systems with interruptions in a single processor environment. While the reachability problem is undecidable for hybrid automata we show that it is decidable for ITA. More precisely we prove that the untimed language of an ITA is regular, by building a finite automaton as a generalized class graph. We then establish that the reachability problem for ITA is in NEXPTIME and in PTIME when the number of clocks is fixed. To prove the first result, we define a subclass ITA- of ITA, and show that (1) any ITA can be reduced to a language-equivalent automaton in ITA- and (2) the reachability problem in this subclass is in NEXPTIME (without any class graph). In the next step, we investigate the verification of real time properties over ITA. We prove that model checking SCL, a fragment of a timed linear time logic, is undecidable. On the other hand, we give model checking procedures for two fragments of timed branching time logic. We also compare the expressive power of classical timed automata and ITA and prove that the corresponding families of accepted languages are incomparable. The result also holds for languages accepted by controlled real-time automata (CRTA), that extend timed automata. We finally combine ITA with CRTA, in a model which encompasses both classes and show that the reachability problem is still decidable. Additionally we show that the languages of ITA are neither closed under complementation nor under intersection