256 research outputs found
A Calculus for Modular Loop Acceleration
Loop acceleration can be used to prove safety, reachability, runtime bounds, and (non-)termination of programs operating on integers. To this end, a variety of acceleration techniques has been proposed. However, all of them are monolithic: Either they accelerate a loop successfully or they fail completely. In contrast, we present a calculus that allows for combining acceleration techniques in a modular way and we show how to integrate many existing acceleration techniques into our calculus. Moreover, we propose two novel acceleration techniques that can be incorporated into our calculus seamlessly. An empirical evaluation demonstrates the applicability of our approach
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 like , , or . 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 where each is a variable, , and each is a (possibly non-linear) polynomial over and the variables . We present a reduction from the question of termination to the existential fragment of the first-order theory of and . For loops over , our reduction entails decidability of termination. For loops over and , 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 , 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
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
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
Observation of the spin-orbit gap in bilayer graphene by one-dimensional ballistic transport
We report on measurements of quantized conductance in gate-defined quantum
point contacts in bilayer graphene that allow the observation of subband
splittings due to spin-orbit coupling. The size of this splitting can be tuned
from 40 to 80 eV by the displacement field. We assign this gate-tunable
subband-splitting to a gap induced by spin-orbit coupling of Kane-Mele type,
enhanced by proximity effects due to the substrate. We show that this
spin-orbit coupling gives rise to a complex pattern in low perpendicular
magnetic fields, increasing the Zeeman splitting in one valley and suppressing
it in the other one. In addition, we observe the existence of a spin-polarized
channel of 6 e/h at high in-plane magnetic field and of signatures of
interaction effects at the crossings of spin-split subbands of opposite spins
at finite magnetic field.Comment: 5 pages, 4 figures, Supplement 6 figure
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