43,042 research outputs found
Abstract Acceleration in Linear relation analysis (extended version)
Linear relation analysis is a classical abstract interpretation based on an over-approximation of reachable numerical states of a program by convex polyhedra. Since it works with a lattice of infinite height, it makes use of a widening operator to enforce the convergence of fixed point computations. Abstract acceleration is a method that computes the precise abstract effect of loops wherever possible and uses widening in the general case. Thus, it improves both the precision and the efficiency of the analysis. This research report gives a comprehensive tutorial on abstract acceleration: its origins in Presburger-based acceleration including new insights w.r.t. the linear accelerability of linear transformations, methods for simple and nested loops, recent extensions, tools and applications, and a detailed discussion of related methods and future perspectives. This is the long version of a paper under submission
Proving Safety with Trace Automata and Bounded Model Checking
Loop under-approximation is a technique that enriches C programs with
additional branches that represent the effect of a (limited) range of loop
iterations. While this technique can speed up the detection of bugs
significantly, it introduces redundant execution traces which may complicate
the verification of the program. This holds particularly true for verification
tools based on Bounded Model Checking, which incorporate simplistic heuristics
to determine whether all feasible iterations of a loop have been considered.
We present a technique that uses \emph{trace automata} to eliminate redundant
executions after performing loop acceleration. The method reduces the diameter
of the program under analysis, which is in certain cases sufficient to allow a
safety proof using Bounded Model Checking. Our transformation is precise---it
does not introduce false positives, nor does it mask any errors. We have
implemented the analysis as a source-to-source transformation, and present
experimental results showing the applicability of the technique
Proving Non-Termination via Loop Acceleration
We present the first approach to prove non-termination of integer programs
that is based on loop acceleration. If our technique cannot show
non-termination of a loop, it tries to accelerate it instead in order to find
paths to other non-terminating loops automatically. The prerequisites for our
novel loop acceleration technique generalize a simple yet effective
non-termination criterion. Thus, we can use the same program transformations to
facilitate both non-termination proving and loop acceleration. In particular,
we present a novel invariant inference technique that is tailored to our
approach. An extensive evaluation of our fully automated tool LoAT shows that
it is competitive with the state of the art
Investigation of friction hysteresis using a laboratory-scale tribometer
The current paper addresses the characterization of dynamic friction by using a laboratory-scale tribometer. A special post-processing script in MatLab has been developed in order to analyse the data from the experiments. A sine wave signal for the velocity is imposed, with three different frequencies and, consequently, acceleration and deceleration rates. A friction material from brakes, with nominal contact area of 254 mm², was subjected to sliding against a commercially available brake disc (gray cast iron, diameter of 256 mm). Some technical details and adjustments from the designed tribometer are showed and the results from the experiments are discussed. A friction hysteresis has been observed for all experimental curves, which exhibit loops in elliptical shape. A negative slope has been encountered for the curves when the imposed frequency is 1 Hz and 2 Hz, while for the highest frequency (4 Hz) the slope is positive. The laboratory-scale tribometer, associated to the post-processing stage, is capable to successfully be used to characterize friction hysteresis effect
Amplification of perpendicular and parallel magnetic fields by cosmic ray currents
Cosmic ray (CR) currents through magnetised plasma drive strong instabilities
producing amplification of the magnetic field. This amplification helps explain
the CR energy spectrum as well as observations of supernova remnants and radio
galaxy hot spots. Using magnetohydrodynamic (MHD) simulations, we study the
behaviour of the non-resonant hybrid (NRH) instability (also known as the Bell
instability) in the case of CR currents perpendicular and parallel to the
initial magnetic field. We demonstrate that extending simulations of the
perpendicular case to 3D reveals a different character to the turbulence from
that observed in 2D. Despite these differences, in 3D the perpendicular NRH
instability still grows exponentially far into the non-linear regime with a
similar growth rate to both the 2D perpendicular and 3D parallel situations. We
introduce some simple analytical models to elucidate the physical behaviour,
using them to demonstrate that the transition to the non-linear regime is
governed by the growth of thermal pressure inside dense filaments at the edges
of the expanding loops. We discuss our results in the context of supernova
remnants and jets in radio galaxies. Our work shows that the NRH instability
can amplify magnetic fields to many times their initial value in parallel and
perpendicular shocks.Comment: Published in MNRAS. 14 pages, 12 figures, 2 tables. Replacement
corrects some typesetting error
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