Multirelations model computations with both angelic and demonic non-determinism. We extend multirelations to represent finite and infinite computations independently. We derive an approximation order for multirelation...
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Multirelations model computations with both angelic and demonic non-determinism. We extend multirelations to represent finite and infinite computations independently. We derive an approximation order for multirelations assuming only that the endless loop is its least element and that the lattice operations are isotone. We use relations, relation algebra and RelView for representing and calculating with multirelations and for finding the approximation order. (C) 2014 Elsevier Inc. All rights reserved.
We give axioms for an operation that describes the states from which a computation has infinite executions in several relational and matrix-based models. The models cover non-strict and strict computations which repre...
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We give axioms for an operation that describes the states from which a computation has infinite executions in several relational and matrix-based models. The models cover non-strict and strict computations which represent finite, infinite and aborting executions with varying precision. Based on the operation we provide an approximation order for a unified description of recursion. Least fixpoints in the approximation order are reduced to least and greatest fixpoints in the underlying semilattice order. We specialise this to a unified description of iteration which satisfies the axioms of a binary operation introduced in previous work. Previous consequences therefore generalise to all discussed computation models in a uniform way. All algebraic results are verified in Isabelle using its integrated automated theorem provers and SMT solvers. (C) 2014 Elsevier Inc. All rights reserved.
With core counts on the rise, the sequential components of applications are becoming the major bottleneck in performance scaling as predicted by Amdahl's law. We are therefore faced with the simultaneous problems ...
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ISBN:
(纸本)9781450309400
With core counts on the rise, the sequential components of applications are becoming the major bottleneck in performance scaling as predicted by Amdahl's law. We are therefore faced with the simultaneous problems of occupying an increasing number of cores and speeding up sequential sections. In this work, we reconcile these two seemingly incompatible problems with a novel programming model called N-way. The core idea behind N-way is to benefit from the algorithmic diversity available to express certain key computational steps. By simultaneously launching in parallel multiple ways to solve a given computation, a runtime can just-in-time pick the best (for example the fastest) way and therefore achieve speedup. Previous work has demonstrated the benefits of such an approach but has not addressed its inherent waste. In this work, we focus on providing a mathematically sound learning-based statistical model that can be used by a runtime to determine the optimal balance between resources used and benefits obtainable through N-way. We further describe a dynamic culling mechanism to further reduce resource waste. We present abstractions and a runtime support to cleanly encapsulate the computational-options and monitor their progress. We demonstrate a low-overhead runtime that achieves significant speedup over a range of widely used kernels. Our results demonstrate super-linear speedups in certain cases.
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