213 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
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
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
U-model based adaptive internal model control for tracking of nonlinear dynamic plants
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
Proving termination of programs automatically with AProVE
AProVE is a system for automatic termination and complexity proofs of Java, C, Haskell, Prolog, and term rewrite systems (TRSs). To analyze programs in high-level languages, AProVE automatically converts them to TRSs. Then, a wide range of techniques is employed to prove termination and to infer complexity bounds for the resulting TRSs. The generated proofs can be exported to check their correctness using automatic certifiers. For use in software construction, we present an AProVE plug-in for the popular Eclipse software development environment
Vicinal Surfaces and the Calogero-Sutherland Model
A miscut (vicinal) crystal surface can be regarded as an array of meandering
but non-crossing steps. Interactions between the steps are shown to induce a
faceting transition of the surface between a homogeneous Luttinger liquid state
and a low-temperature regime consisting of local step clusters in coexistence
with ideal facets. This morphological transition is governed by a hitherto
neglected critical line of the well-known Calogero-Sutherland model. Its exact
solution yields expressions for measurable quantities that compare favorably
with recent experiments on Si surfaces.Comment: 4 pages, revtex, 2 figures (.eps
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