174 research outputs found
Higher-order linearisability
Linearisability is a central notion for verifying concurrent libraries: a library is proven correct if its operational history can be rearranged into a sequential one that satisfies a given specification. Until now, linearisability has been examined for libraries in which method arguments and method results were of ground type. In this paper we extend linearisability to the general higher-order setting, where methods of arbitrary type can be passed as arguments and returned as values, and establish its soundness
Higher-Order Linearisability
Linearisability is a central notion for verifying concurrent libraries: a library is proven
correct if its operational history can be rearranged into a sequential one that satisfies a
given specification. Until now, linearisability has been examined for libraries in which
method arguments and method results were of ground type. In this paper we extend
linearisability to the general higher-order setting, where methods of arbitrary type can
be passed as arguments and returned as values, and establish its soundness
Steps in modular specifications for concurrent modules
© 2015 Published by Elsevier B.V.The specification of a concurrent program module is a difficult problem. The specifications must be strong enough to enable reasoning about the intended clients without reference to the underlying module implementation. We survey a range of verification techniques for specifying concurrent modules, in particular highlighting four key concepts: auxiliary state, interference abstraction, resource ownership and atomicity. We show how these concepts combine to provide powerful approaches to specifying concurrent modules
On the integrability of symplectic Monge-Amp\'ere equations
Let u be a function of n independent variables x^1, ..., x^n, and U=(u_{ij})
the Hessian matrix of u. The symplectic Monge-Ampere equation is defined as a
linear relation among all possible minors of U. Particular examples include the
equation det U=1 governing improper affine spheres and the so-called heavenly
equation, u_{13}u_{24}-u_{23}u_{14}=1, describing self-dual Ricci-flat
4-manifolds. In this paper we classify integrable symplectic Monge-Ampere
equations in four dimensions (for n=3 the integrability of such equations is
known to be equivalent to their linearisability). This problem can be
reformulated geometrically as the classification of 'maximally singular'
hyperplane sections of the Plucker embedding of the Lagrangian Grassmannian. We
formulate a conjecture that any integrable equation of the form F(u_{ij})=0 in
more than three dimensions is necessarily of the symplectic Monge-Ampere type.Comment: 20 pages; added more details of proof
On a class of integrable systems of Monge-Amp\`ere type
We investigate a class of multi-dimensional two-component systems of
Monge-Amp\`ere type that can be viewed as generalisations of heavenly-type
equations appearing in self-dual Ricci-flat geometry. Based on the
Jordan-Kronecker theory of skew-symmetric matrix pencils, a classification of
normal forms of such systems is obtained. All two-component systems of
Monge-Amp\`ere type turn out to be integrable, and can be represented as the
commutativity conditions of parameter-dependent vector fields. Geometrically,
systems of Monge-Amp\`ere type are associated with linear sections of the
Grassmannians. This leads to an invariant differential-geometric
characterisation of the Monge-Amp\`ere property.Comment: arXiv admin note: text overlap with arXiv:1503.0227
Straightening warped cones
We provide the converses to two results of J. Roe (Geom. Topol. 2005): first,
the warped cone associated to a free action of an a-T-menable group admits a
fibred coarse embedding into a Hilbert space, and second, a free action
yielding a warped cone with property A must be amenable. We construct examples
showing that in both cases the freeness assumption is necessary. The first
equivalence is obtained also for other classes of Banach spaces, in particular
for -spaces.Comment: Final authors' version of the article published by JTA. Changes since
v2: the proof of Lem. 3.8 (now Prop. 3.10) is split between several lemmata,
the proof of Thm 4.2 simplified and more detaile
On library correctness under weak memory consistency: specifying and verifying concurrent libraries under declarative consistency models
Concurrent libraries are the building blocks for concurrency. They encompass a range of abstractions (locks, exchangers, stacks, queues, sets) built in a layered fashion: more advanced libraries are built out of simpler ones. While there has been a lot of work on verifying such libraries in a sequentially consistent (SC) environment, little is known about how to specify and verify them under weak memory consistency (WMC). We propose a general declarative framework that allows us to specify concurrent libraries declaratively, and to verify library implementations against their specifications compositionally. Our framework is sufficient to encode standard models such as SC, (R)C11 and TSO. Additionally, we specify several concurrent libraries, including mutual exclusion locks, reader-writer locks, exchangers, queues, stacks and sets. We then use our framework to verify multiple weakly consistent implementations of locks, exchangers, queues and stacks
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