In this paper, we consider the “foreach” sparse recovery problem with failure probability p. The goalof which is to design a distribution over m × N matrices Φ and a decoding algorithm A such that forevery x ∈ R , we have the following error guarantee with probability at least 1− p‖x−A(Φx)‖2 6 C‖x− xk‖2,where C is a constant (ideally arbitrarily close to 1) and xk is the best k-...

We describe the implementation of specific Scala collections operations (currently the map and foreach methods) using the Scala 2.10 compile-time reflection facilities. The primary motivation for this work is to create faster collections by inlining operations at the call site. The functionality is available at the standard Scala library level, so that our optimized operations can be used on al...

ion before(task(Si,Di), task(Sj,Dj)) :Si+Di #<= Sj. Conjunction between(X,Y,Z) :X #< Y, Y #< Z. Disjunction (but see below) neighbour(X,Y) :( X #= Y+1 ; Y #= X+1 ). Iteration not_among(X, L) :( foreach(Y,L),param(X) do X #\= Y ). Recursion not_among(X, []). not_among(X, [Y|Ys]) :X #\= Y, not_among(X, Ys). 11.4 Same Problem Different Model There are often many ways of modelling a problem. Consid...

We provide a framework for program and data refinement in Isabelle/HOL. The framework is based on a nondeterminism-monad with assertions, i.e., the monad carries a set of results or an assertion failure. Recursion is expressed by fixed points. For convenience, we also provide while and foreach combinators. The framework provides tools to automatize canonical tasks, such as verification conditio...

code for the sensor is shown in Program 2. It repeatedly obtains multi-spectral image cubes from the sensor (1), waits for an appropriate request for work from a worker (2), decomposes the image cube to generate an unassigned sub-cube (3) and sends the sub-cube to the requesting worker (4). Program 2: Sensor Thread Operation main() { mp = get_my_multiprocessor_id() if(mp == 0) { numsubcubes = g...

The data parallel programming language construct of a “foreach” loop is proposed in the context of hierarchically nested arrays and unbalanced k-ary trees used in high performance applications. In order perform an initial evaluation, an implementation of an automatic parallelization system for C++ programs is introduced, which consists of a preprocessor and a matching library for distributed me...

ion before(task(Si,Di), task(Sj,Dj)) :Si+Di #<= Sj. Conjunction between(X,Y,Z) :X #< Y, Y #< Z. Disjunction (but see below) neighbour(X,Y) :( X #= Y+1 ; Y #= X+1 ). Iteration not_among(X, L) :( foreach(Y,L),param(X) do X #\= Y ). Recursion not_among(X, []). not_among(X, [Y|Ys]) :X #\= Y, not_among(X, Ys). 11.4 Same Problem Different Model There are often many ways of modelling a problem. Consid...

ion before(task(Si,Di), task(Sj,Dj)) :Si+Di #<= Sj. Conjunction between(X,Y,Z) :X #< Y, Y #< Z. Disjunction (but see below) neighbour(X,Y) :( X #= Y+1 ; Y #= X+1 ). Iteration not_among(X, L) :( foreach(Y,L),param(X) do X #\= Y ). Recursion not_among(X, []). not_among(X, [Y|Ys]) :X #\= Y, not_among(X, Ys). 11.4 Same Problem Different Model There are often many ways of modelling a problem. Consid...

ion before(task(Si,Di), task(Sj,Dj)) :Si+Di #<= Sj. Conjunction between(X,Y,Z) :X #< Y, Y #< Z. Disjunction (but see below) neighbour(X,Y) :( X #= Y+1 ; Y #= X+1 ). Iteration not_among(X, L) :( foreach(Y,L),param(X) do X #\= Y ). Recursion not_among(X, []). not_among(X, [Y|Ys]) :X #\= Y, not_among(X, Ys). 11.4 Same Problem Different Model There are often many ways of modelling a problem. Consid...