Termination of Triangular Integer Loops is Decidable

We consider the problem whether termination of affine integer loops is decidable. Since Tiwari conjectured decidability in 2004, only special cases have been solved. We complement this work by proving decidability for the case that the update matrix is triangular

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

On the Decidability of Termination for Polynomial Loops

We consider the termination problem for triangular weakly non-linear loops (twn-loops) over some ring $\mathcal{S}$ like $\mathbb{Z}$, $\mathbb{Q}$, or $\mathbb{R}$. Essentially, the guard of such a loop is an arbitrary Boolean formula over (possibly non-linear) polynomial inequations, and the body is a single assignment $(x_1, \ldots, x_d) \longleftarrow (c_1 \cdot x_1 + p_1, \ldots, c_d \cdot x_d + p_d)$ where each $x_i$ is a variable, $c_i \in \mathcal{S}$, and each $p_i$ is a (possibly non-linear) polynomial over $\mathcal{S}$ and the variables $x_{i+1},\ldots,x_{d}$. We present a reduction from the question of termination to the existential fragment of the first-order theory of $\mathcal{S}$ and $\mathbb{R}$. For loops over $\mathbb{R}$, our reduction entails decidability of termination. For loops over $\mathbb{Z}$ and $\mathbb{Q}$, it proves semi-decidability of non-termination. Furthermore, we present a transformation to convert certain non-twn-loops into twn-form. Then the original loop terminates iff the transformed loop terminates over a specific subset of $\mathbb{R}$, which can also be checked via our reduction. This transformation also allows us to prove tight complexity bounds for the termination problem for two important classes of loops which can always be transformed into twn-loops

Modelling transport and deposition of caesium and iodine from the Chernobyl accident using the DREAM model

International audienceA tracer model, DREAM (the Danish Rimpuff and Eulerian Accidental release Model), has been developed for modelling transport, dispersion and deposition (wet and dry) of radioactive material from accidental releases, as the Chernobyl accident. The model is a combination of a Lagrangian model, that includes the near source dispersion, and an Eulerian model describing the long-range transport. The performance of the transport model has previously been tested within the European Tracer Experiment, ETEX, which included transport and dispersion of an inert, non-depositing tracer from a controlled release. The focus of this paper is the model performance with respect to the deposition of 137Cs, 134Cs and 131I from the Chernobyl accident, using different relatively simple and comprehensive parameterizations. The performance, compared to measurements, of different combinations of parameterizations of wet and dry deposition schemes has been evaluated, using different statistical tests

Le logement communautaire au Québec : apports et limites d’une innovation sociale

Le logement communautaire constitue au Québec une alternative au logement privé à but lucratif et au logement public subventionné de type HLM. Il s’agit d’un logement de propriété collective incarnée soit par une coopérative d’habitation, soit par un organisme sans but lucratif (OSBL) d’habitation. Ces deux formules juridiques, la coopérative et l’association, en plus d’offrir des logements accessibles financièrement, contribuent à la prise en charge de leur milieu de vie par les résidants en favorisant la participation, directe ou indirecte, de ces derniers à la gestion de leur ensemble résidentiel. La réalisation de ce type de logement implique l’engagement d’acteurs de la société civile, l’apport de fonds publics et une remise en cause de la logique marchande. Le logement communautaire représente ainsi une innovation sociale sur le plan des rapports de consommation, de production et de gouvernance. Nous mettons en lumière, dans cet article, non seulement les apports, mais aussi les limites de cette triple innovation sociale qui s’inscrit dans un mode de régulation associatif du logement.In Quebec, community housing is an alternative to private for-profit housing and to publicly funded low-income housing. It is collectively owned housing that takes the form of either a housing cooperative or a housing non-profit organization (NPO). These two legal forms of organization, the cooperative and the association, besides providing affordable housing, encourage residents to take responsibility for the area where they live by fostering their direct or indirect participation in the management of their housing complex. Creating this type of housing requires the involvement of civil society stakeholders, the availability of public funds and a willingness to question the logic of the marketplace. Community housing thus represents a social innovation on the consumer, production and governance levels. In this paper, we highlight not only the benefits, but also the limitations of this threefold social innovation characteristic of an association-based form of housing regulation

Modelling of Mercury in the Arctic with the Danish Eulerian Hemispheric Model

International audienceA new 3-D mercury model has been developed within the Danish Arctic Monitoring and Assessment Programme (AMAP). The model is based on the Danish Eulerian Hemispheric Model, which in the original version has been used to study the transport of SO2, SO42- and Pb into the Arctic. It was developed for sulphur in 1990 and in 1999 also lead was included. For the current study a chemical scheme for mercury has been included and the model is now applied to the mercury transport problem. Some experiments with the formulation of the mercury chemistry during the Polar Sunrise are carried out in order to investigate the observed depletion. Some of the main conclusions of the work described in this paper are that atmospheric transport of mercury is a very important pathway into the Arctic and that mercury depletion in the Arctic troposphere during the Polar Sunrise contributes considerably to the deposition of mercury in the Arctic

Modelling of mercury with the Danish Eulerian Hemispheric Model

International audienceA new 3-D mercury model has been developed within the Danish Arctic Monitoring and Assessment Programme (AMAP). The model is based on the Danish Eulerian Hemispheric Model, which in the original version has been used to study the transport of SO2, SO42? and Pb into the Arctic. It was developed for sulphur in 1990 and in 1999 also lead was included. For the current study a chemical scheme for mercury has been included and the model is now applied to the mercury transport problem. Some experiments with the formulation of the mercury chemistry during the Polar Sunrise are carried out in order to investigate the observed depletion. Some of the main conclusions of the work described in this paper are that atmospheric transport of mercury is a very important pathway into the Arctic and that mercury depletion in the Arctic troposphere during the Polar Sunrise contributes considerably to the deposition of mercury in the Arctic

Termination of Triangular Integer Loops is Decidable

We consider the problem whether termination of affine integer loops is decidable. Since Tiwari conjectured decidability in 2004, only special cases have been solved. We complement this work by proving decidability for the case that the update matrix is triangular.Comment: Full version (with proofs) of a paper published in the Proceedings of the 31st International Conference on Computer Aided Verification (CAV '19), New York, NY, USA, Lecture Notes in Computer Science, Springer-Verlag, 201

Inferring Lower Runtime Bounds for Integer Programs

We present a technique to infer lower bounds on the worst-case runtime complexity of integer programs, where in contrast to earlier work, our approach is not restricted to tail-recursion. Our technique constructs symbolic representations of program executions using a framework for iterative, under-approximating program simplification. The core of this simplification is a method for (under-approximating) program acceleration based on recurrence solving and a variation of ranking functions. Afterwards, we deduce asymptotic lower bounds from the resulting simplified programs using a special-purpose calculus and an SMT encoding. We implemented our technique in our tool LoAT and show that it infers non-trivial lower bounds for a large class of examples

Wind dispersal of genetically modified pollen from oilseed rape and rye fields

The increasing use of genetically modified plants (GMP) has opened up for a discussion about the problems related to the co-existence of GM and non-GM crops and especially the consequences for organic farming. One of the objectives of DARCOF project TOPRO (Tool for protection against contamination by GMO) has been to develop specific modelling tools, which can be used for the prediction of dispersal of GM pollen under different conditions and for investigating measures to limit the GM dispersal to organic fields