13,103 research outputs found
Pathwise Accuracy and Ergodicity of Metropolized Integrators for SDEs
Metropolized integrators for ergodic stochastic differential equations (SDE)
are proposed which (i) are ergodic with respect to the (known) equilibrium
distribution of the SDE and (ii) approximate pathwise the solutions of the SDE
on finite time intervals. Both these properties are demonstrated in the paper
and precise strong error estimates are obtained. It is also shown that the
Metropolized integrator retains these properties even in situations where the
drift in the SDE is nonglobally Lipschitz, and vanilla explicit integrators for
SDEs typically become unstable and fail to be ergodic.Comment: 46 pages, 5 figure
Hoare-style Specifications as Correctness Conditions for Non-linearizable Concurrent Objects
Designing scalable concurrent objects, which can be efficiently used on
multicore processors, often requires one to abandon standard specification
techniques, such as linearizability, in favor of more relaxed consistency
requirements. However, the variety of alternative correctness conditions makes
it difficult to choose which one to employ in a particular case, and to compose
them when using objects whose behaviors are specified via different criteria.
The lack of syntactic verification methods for most of these criteria poses
challenges in their systematic adoption and application.
In this paper, we argue for using Hoare-style program logics as an
alternative and uniform approach for specification and compositional formal
verification of safety properties for concurrent objects and their client
programs. Through a series of case studies, we demonstrate how an existing
program logic for concurrency can be employed off-the-shelf to capture
important state and history invariants, allowing one to explicitly quantify
over interference of environment threads and provide intuitive and expressive
Hoare-style specifications for several non-linearizable concurrent objects that
were previously specified only via dedicated correctness criteria. We
illustrate the adequacy of our specifications by verifying a number of
concurrent client scenarios, that make use of the previously specified
concurrent objects, capturing the essence of such correctness conditions as
concurrency-aware linearizability, quiescent, and quantitative quiescent
consistency. All examples described in this paper are verified mechanically in
Coq.Comment: 18 page
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