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

Effect of phenylephrine on pyruvate dehydrogenase activity in rat hepatocytes and its interaction with insulin and glucagon

AbstractIn isolated rat hepatocytes phenylephrine promotes a rapid increase in the amount of pyruvate dehydrogenase present in its active form (PDHa). This action is mediated by α1-adrenergic receptors and is not observed in Ca2+-depleted hepatocytes. It is mimicked by the Ca2+ ionophore A23187. No changes in metabolites known to affect PDH activity are measured 3 min after addition of phenylephrine. Glucagon also increases PDHa, its action is additive to that of phenylephrine. The action of phenylephrine on PDHa could be explained by an increase in mitochondrial free Ca2+

A simple abstraction of arrays and maps by program translation

We present an approach for the static analysis of programs handling arrays, with a Galois connection between the semantics of the array program and semantics of purely scalar operations. The simplest way to implement it is by automatic, syntactic transformation of the array program into a scalar program followed analysis of the scalar program with any static analysis technique (abstract interpretation, acceleration, predicate abstraction,.. .). The scalars invariants thus obtained are translated back onto the original program as universally quantified array invariants. We illustrate our approach on a variety of examples, leading to the " Dutch flag " algorithm

Abstract Interpretation with Unfoldings

We present and evaluate a technique for computing path-sensitive interference conditions during abstract interpretation of concurrent programs. In lieu of fixed point computation, we use prime event structures to compactly represent causal dependence and interference between sequences of transformers. Our main contribution is an unfolding algorithm that uses a new notion of independence to avoid redundant transformer application, thread-local fixed points to reduce the size of the unfolding, and a novel cutoff criterion based on subsumption to guarantee termination of the analysis. Our experiments show that the abstract unfolding produces an order of magnitude fewer false alarms than a mature abstract interpreter, while being several orders of magnitude faster than solver-based tools that have the same precision.Comment: Extended version of the paper (with the same title and authors) to appear at CAV 201

A certifying frontend for (sub)polyhedral abstract domains

Convex polyhedra provide a relational abstraction of numerical properties for static analysis of programs by abstract interpretation. We describe a lightweight certification of polyhedral abstract domains using the Coq proof assistant. Our approach consists in delegating most computations to an untrusted backend and in checking its outputs with a certified frontend. The backend is free to implement relaxations of domain operators in order to trade some precision for more efficiency, but must produce hints about the soundness of its results. Experiments with a full-precision backend show that the certification overhead is small and that the certified abstract domain has comparable performance to non-certifying state-of-the-art implementations

The STARTWAVE atmospheric water database

International audienceThe STARTWAVE (STudies in Atmospheric Radiative Transfer and Water Vapour Effects) project aims to investigate the role which water vapour plays in the climate system, and in particular its interaction with radiation. Within this framework, an ongoing water vapour database project was set up which comprises integrated water vapour (IWV) measurements made over the last ten years by ground-based microwave radiometers, Global Positioning System (GPS) receivers and sun photometers located throughout Switzerland at altitudes between 330 and 3584 m. At Bern (46.95° N, 7.44° E) tropospheric and stratospheric water vapour profiles are obtained on a regular basis and integrated liquid water, which is important for cloud characterisation, is also measured. Additional stratospheric water vapour profiles are obtained by an airborne microwave radiometer which observes large parts of the northern hemisphere during yearly flight campaigns. The database allows us to validate the various water vapour measurement techniques. Comparisons between IWV measured by the Payerne radiosonde with that measured at Bern by two microwave radiometers, GPS and sun photometer showed instrument biases within ±0.5 mm. The bias in GPS relative to sun photometer over the 2001 to 2004 period was ?0.8 mm at Payerne (46.81° N, 6.94° E, 490 m), which lies in the Swiss plains north of the Alps, and +0.6 mm at Davos (46.81° N, 9.84° E, 1598 m), which is located within the Alps in the eastern part of Switzerland. At Locarno (46.18° N, 8.78° E, 366 m), which is located on the south side of the Alps, the bias is +1.9 mm. The sun photometer at Locarno was found to have a bias of ?2.2 mm (13% of the mean annual IWV) relative to the data from the closest radiosonde station at Milano. This result led to a yearly rotation of the sun photometer instruments between low and high altitude stations to improve the calibrations. In order to demonstrate the capabilites of the database for studying water vapour variations, we investigated a front which crossed Switzerland between 18 November 2004 and 19 November 2004. During the frontal passage, the GPS and microwave radiometers at Bern and Payerne showed an increase in IWV of between 7 and 9 mm. The GPS IWV measurements were corrected to a standard height of 500 m, using an empirically derived exponential relationship between IWV and altitude. A qualitative comparison was made between plots of the IWV distribution measured by the GPS and the 6.2 µm water vapour channel on the Meteosat Second Generation (MSG) satellite. Both showed that the moist air moved in from a northerly direction, although the MSG showed an increase in water vapour several hours before increases in IWV were detected by GPS or microwave radiometer. This is probably due to the fact that the satellite instrument is sensitive to an atmospheric layer at around 320 hPa, which makes a contribution of one percent or less to the IWV

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