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

Очистка воды от солей жёсткости при помощи бытового водоочитстного фильтра

В работе проведено исследование фильтра-кувшина Аквафор Гарри, при процессах динамической фильтрации, через него водопроводной воды содержащей соли жёсткости. Определена степень извлечения солей жёсткости и ресурс исследуемого картриджа В100-8.In this work, a study of the filter-jar Aquaphor Harry was carried out in the process of dynamic filtration of tap water containing hardness salts. The degree of extraction of hardness salts and the working life of the investigated cartridge B100-8 was determined

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

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

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

Wohnregal Building, Berlin, Germany [Edificio Wohnregal, Berlín, Alemania]

It is not very common for residential buildings to express the layout of their structural resistance so clearly. But when it comes to precast concrete systems - such as the one used by this building - the necessary dilatations between the different elements requires the load exchange to be evident. Thus, the visibility of the structural system becomes the protagonist of absolutely neutral and flexible interiors

Modelling atmospheric transport of ?-hexachlorocyclohexane in the Northern Hemispherewith a 3-D dynamical model: DEHM-POP

International audienceThe Danish Eulerian Hemispheric Model (DEHM) is a 3-D dynamical atmospheric transport model originally developed to describe the atmospheric transport of sulphur into the Arctic. A new version of the model, DEHM-POP, developed to study the atmospheric transport and environmental fate of persistent organic pollutants (POPs) is presented. During environmental cycling, POPs can be deposited and re-emitted several times before reaching a final destination. A description of the exchange processes between the land/ocean surfaces and the atmosphere is included in the model to account for this multi-hop transport. The ?-isomer of the pesticide hexachlorocyclohexane (?-HCH) is used as tracer in the model development. The structure of the model and processes included are described in detail. The results from a model simulation showing the atmospheric transport for the years 1991 to 1998 are presented and evaluated against measurements. The annual averaged atmospheric concentration of ?-HCH for the 1990s is well described by the model; however, the shorter-term average concentration for most of the stations is not well captured. This indicates that the present simple surface description needs to be refined to get a better description of the air-surface exchange processes of POPs

Modelling atmospheric transport of persistent organic pollutants in the Northern Hemisphere with a 3-D dynamical model: DEHM-POP

International audienceThe Danish Eulerian Hemispheric Model (DEHM) is a 3-D dynamical atmospheric transport model originally developed to describe the atmospheric transport of sulphur into the Arctic. A new version of the model, DEHM-POP, developed to study the atmospheric transport and environmental fate of persistent organic pollutants (POPs) is presented. During environmental cycling, POPs can be deposited and re-emitted several times before reaching a final destination. A description of the exchange processes between the land/ocean surfaces and the atmosphere is included in the model to account for this multi-hop transport. The ?-isomer of the pesticide hexachlorocyclohexane (?-HCH) is used as tracer in the model development. The structure of the model and processes included are described in detail. The results from a model simulation showing the atmospheric transport for the years 1991 to 1998 are presented and evaluated against measurements. The annual averaged atmospheric concentration of ?-HCH for the 1990s is well described by the model; however, the shorter-term average concentration for most of the stations is not well captured. This indicates that the present simple surface description needs to be refined to get a better description of the air-surface exchange proceses of POPs