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Mapping a Functional Notation for Parallel Programs onto Hypercubes
 Information Processing Letters
, 1995
"... The theory of powerlists was recently introduced by Jayadev Misra [7]. Powerlists can be used to specify and verify certain parallel algorithms, using a notation similar to functional programming languages. In contrast to sequential languages the powerlist notation has constructs for expressing bala ..."
Abstract

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The theory of powerlists was recently introduced by Jayadev Misra [7]. Powerlists can be used to specify and verify certain parallel algorithms, using a notation similar to functional programming languages. In contrast to sequential languages the powerlist notation has constructs for expressing balanced divisions of lists. We study how Prefix Sum, a fundamental parallel algorithm, can be tailored for efficient execution on hypercubic architectures. Then we derive a strategy for mapping most powerlist functions to efficient programs for hypercubic architectures. Keywords: Program derivation; Parallel algorithms; Functional programming; Programming calculi; Hypercubes; Prefix sum 1 Introduction The field of parallel algorithm design has become a major area of research over the last decade. However, the field has yet to develop a standard language for expressing these algorithms. The Powerlist notation, introduced by Jayadev Misra [7], gives us a succinct representation of a certain clas...
Data Structures for Parallel Recursion
, 1997
"... vii Chapter 1 Introduction 1 1.1 Synchronous Parallel Programming . . . . . . . . . . . . . . . . . . . 4 1.2 Basic Definitions and Notations . . . . . . . . . . . . . . . . . . . . . 6 1.2.1 Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.2 Operator Priority . . . . . . . ..."
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Cited by 2 (0 self)
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vii Chapter 1 Introduction 1 1.1 Synchronous Parallel Programming . . . . . . . . . . . . . . . . . . . 4 1.2 Basic Definitions and Notations . . . . . . . . . . . . . . . . . . . . . 6 1.2.1 Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.2 Operator Priority . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.3 Notation and Proof Style . . . . . . . . . . . . . . . . . . . . 9 1.3 Cost Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.3.1 Parallel Algorithm Complexity . . . . . . . . . . . . . . . . . 14 1.3.2 Parallel Computation Models . . . . . . . . . . . . . . . . . . 17 Chapter 2 Powerlists 20 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.1.1 Induction Principle for PowerLists . . . . . . . . . . . . . . . . 25 2.1.2 Data Movement and Permutation Functions . . . . . . . . . . 26 2.2 Hypercubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.3 A Cost Calculus for P...
On "An O(log N) Algorithm to Solve Linear Recurrences on Hypercubes"
, 1994
"... this paper is that solving the linear recurrence problem can be reduced to an instance of prefix sum. This follows from the following theorem: ..."
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this paper is that solving the linear recurrence problem can be reduced to an instance of prefix sum. This follows from the following theorem: