Logico-numerical max-strategy iteration

Strategy iteration methods are used for solving fixed point equations. It has been shown that they improve precision in static analysis based on abstract interpretation and template abstract domains, e.g. intervals, octagons or template polyhedra. However, they are limited to numerical programs. In this paper, we propose a method for applying max-strategy iteration to logico-numerical programs, i.e. programs with numerical and Boolean variables, without explicitly enumerating the Boolean state space. The method is optimal in the sense that it computes the least fixed point w.r.t. the abstract domain; in particular, it does not resort to widening. Moreover, we give experimental evidence about the efficiency and precision of the approach

Improving Strategies via SMT Solving

We consider the problem of computing numerical invariants of programs by abstract interpretation. Our method eschews two traditional sources of imprecision: (i) the use of widening operators for enforcing convergence within a finite number of iterations (ii) the use of merge operations (often, convex hulls) at the merge points of the control flow graph. It instead computes the least inductive invariant expressible in the domain at a restricted set of program points, and analyzes the rest of the code en bloc. We emphasize that we compute this inductive invariant precisely. For that we extend the strategy improvement algorithm of [Gawlitza and Seidl, 2007]. If we applied their method directly, we would have to solve an exponentially sized system of abstract semantic equations, resulting in memory exhaustion. Instead, we keep the system implicit and discover strategy improvements using SAT modulo real linear arithmetic (SMT). For evaluating strategies we use linear programming. Our algorithm has low polynomial space complexity and performs for contrived examples in the worst case exponentially many strategy improvement steps; this is unsurprising, since we show that the associated abstract reachability problem is Pi-p-2-complete

Succinct Representations for Abstract Interpretation

Abstract interpretation techniques can be made more precise by distinguishing paths inside loops, at the expense of possibly exponential complexity. SMT-solving techniques and sparse representations of paths and sets of paths avoid this pitfall. We improve previously proposed techniques for guided static analysis and the generation of disjunctive invariants by combining them with techniques for succinct representations of paths and symbolic representations for transitions based on static single assignment. Because of the non-monotonicity of the results of abstract interpretation with widening operators, it is difficult to conclude that some abstraction is more precise than another based on theoretical local precision results. We thus conducted extensive comparisons between our new techniques and previous ones, on a variety of open-source packages.Comment: Static analysis symposium (SAS), Deauville : France (2012

A hard x ray split and delay unit for the HED experiment at the European XFEL

For the High Energy Density HED experiment [1] at the European XFEL [2] an x ray split and delay unit SDU is built covering photon energies from 5 keV up to 20 keV [3]. This SDU will enable time resolved x ray pump x ray probe experiments [4,5] as well as sequential diffractive imaging [6] on a femtosecond to picosecond time scale. Further, direct measurements of the temporal coherence properties will be possible by making use of a linear autocorrelation [7,8]. The set up is based on geometric wavefront beam splitting, which has successfully been implemented at an autocorrelator at FLASH [9]. The x ray FEL pulses are split by a sharp edge of a silicon mirror coated with multilayers. Both partial beams will then pass variable delay lines. For different photon energies the angle of incidence onto the multilayer mirrors will be adjusted in order to match the Bragg condition. For a photon energy of h amp; 957; 20 keV a grazing angle of amp; 952; 0.57 has to be set, which results in a footprint of the beam 6 amp; 963; on the mirror of l 98 mm. At this photon energy the reflectance of a Mo B4C multi layer coating with a multilayer period of d 3.2 nm and N 200 layers amounts to R 0.92. In order to enhance the maximum transmission for photon energies of h amp; 957; 8 keV and below, a Ni B4C multilayer coating can be applied beside the Mo B4C coating for this spectral region. Because of the different incidence angles, the path lengths of the beams will differ as a function of wavelength. Hence, maximum delays between 2.5 ps at h amp; 957; 20 keV and up to 23 ps at h amp; 957; 5 keV will be possibl

Using Bounded Model Checking to Focus Fixpoint Iterations

Two classical sources of imprecision in static analysis by abstract interpretation are widening and merge operations. Merge operations can be done away by distinguishing paths, as in trace partitioning, at the expense of enumerating an exponential number of paths. In this article, we describe how to avoid such systematic exploration by focusing on a single path at a time, designated by SMT-solving. Our method combines well with acceleration techniques, thus doing away with widenings as well in some cases. We illustrate it over the well-known domain of convex polyhedra

Constrained Dynamic Tree Networks

We generalise Constrained Dynamic Pushdown Networks, introduced by Bouajjani\et al, to Constrained Dynamic Tree Networks.<br>In this model, we have trees of processes which may monitor their children.<br>We allow the processes to be defined by any computation model for which the alternating reachability problem is decidable.<br>We address the problem of symbolic reachability analysis for this model. More precisely, we consider the problem of computing an effective representation of their reachability<br>sets using finite state automata. <div>We show that backwards reachability sets starting from regular sets of configurations are always regular. </div><div>We provide an algorithm for computing backwards reachability sets using tree automata.<br><br></div

Determination of nutrient salts by automatic methods both in seawater and brackish water: the phosphate blank

9 páginas, 2 tablas, 2 figurasThe main inconvenience in determining nutrients in seawater by automatic methods is simply solved: the preparation of a suitable blank which corrects the effect of the refractive index change on the recorded signal. Two procedures are proposed, one physical (a simple equation to estimate the effect) and the other chemical (removal of the dissolved phosphorus with ferric hydroxide).Support for this work came from CICYT (MAR88-0245 project) and Conselleria de Pesca de la Xunta de GaliciaPeer reviewe

Template-Based Unbounded Time Verification of Affine Hybrid Automata

Computing over-approximations of all possible time trajectories is an important task in the analysis of hybrid systems. Sankaranarayanan et al. [20] suggested to approximate the set of reachable states using template polyhedra. In the present paper, we use a max-strategy improvement algorithm for computing an abstract semantics for affine hybrid automata that is based on template polyhedra and safely over-approximates the concrete semantics. Based on our formulation, we show that the corresponding abstract reachability problem is in co−NP. Moreover, we obtain a polynomial-time algorithm for the time elapse operation over template polyhedra