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

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

Coarse abstractions make Zeno behaviours difficult to detect

An infinite run of a timed automaton is Zeno if it spans only a finite amount of time. Such runs are considered unfeasible and hence it is important to detect them, or dually, find runs that are non-Zeno. Over the years important improvements have been obtained in checking reachability properties for timed automata. We show that some of these very efficient optimizations make testing for Zeno runs costly. In particular we show NP-completeness for the LU-extrapolation of Behrmann et al. We analyze the source of this complexity in detail and give general conditions on extrapolation operators that guarantee a (low) polynomial complexity of Zenoness checking. We propose a slight weakening of the LU-extrapolation that satisfies these conditions

Using non-convex approximations for efficient analysis of timed automata

The reachability problem for timed automata asks if there exists a path from an initial state to a target state. The standard solution to this problem involves computing the zone graph of the automaton, which in principle could be infinite. In order to make the graph finite, zones are approximated using an extrapolation operator. For reasons of efficiency in current algorithms extrapolation of a zone is always a zone and in particular it is convex. In this paper, we propose to solve the reachability problem without such extrapolation operators. To ensure termination, we provide an efficient algorithm to check if a zone is included in the so called region closure of another. Although theoretically better, closure cannot be used in the standard algorithm since a closure of a zone may not be convex. An additional benefit of the proposed approach is that it permits to calculate approximating parameters on-the-fly during exploration of the zone graph, as opposed to the current methods which do it by a static analysis of the automaton prior to the exploration. This allows for further improvements in the algorithm. Promising experimental results are presented.Comment: Extended version of FSTTCS 2011 pape

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

Impaired RNA incorporation and dimerization in live attenuated leader-variants of SIV(mac239)

BACKGROUND: The 5' untranslated region (UTR) or leader sequence of simian immunodeficiency virus (SIV(mac239)) is multifunctional and harbors the regulatory elements for viral replication, persistence, gene translation, expression, and the packaging and dimerization of viral genomic RNA (vRNA). We have constructed a series of deletions in the SIV(mac239 )leader sequence in order to determine the involvement of this region in both the packaging and dimerization of viral genomic RNA. We also assessed the impact of these deletions upon viral infectiousness, replication kinetics and gene expression in cell lines and monkey peripheral blood mononuclear cells (PBMC). RESULTS: Regions on both sides of the major splice donor (SD) were found to be necessary for the efficiency and specificity of viral genome packaging. However, stem-loop1 is critical for both RNA encapsidation and dimerization. Downstream elements between the splice donor and the initiation site of SIV-Gag have additive effects on RNA packaging and contribute to a lesser degree to RNA dimerization. The targeted disruption of structures on both sides of the SD also severely impacts viral infectiousness, gene expression and replication in both CEMx174 cells and rhesus PBMC. CONCLUSION: In the leader region of SIV(mac239), stem-loop1 functions as the primary determinant for both RNA encapsidation and dimerization. Downstream elements between the splice donor and the translational initiation site of SIV-Gag are classified as secondary determinants and play a role in dimerization. Collectively, these data signify a linkage between the primary encapsidation determinant of SIV(mac239 )and RNA dimerization