Variations on Constants : Flow Analysis of Sequential and Parallel Programs - Markus MÃ¼ller-Olm

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Variations on Constants

Flow Analysis of Sequential and Parallel Programs

By: Markus MÃ¼ller-Olm

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Paperback | 2 October 2006

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196 Pages

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22.86 x 15.24 x 1.27

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Program analysis is concerned with techniques that automatically determine run-time properties of given programs prior to run-time. It is used for validation in order to ensure that programs serve their intended purpose and in further processing for efficient execution such as in optimizing compilers. Optimal program analysis provides a guarantee about the precision of the computed results.

This monograph, a revised version of the author's habilitation thesis, focusses on optimal flow analysis of sequential and parallel programs. It studies algorithmic properties of various versions of the well-known constant-propagation problem. In order to come to grips with the variants considered, it combines techniques from different areas such as linear algebra, computable ring theory, abstract interpretation, program verification, complexity theory, etc. Combination of techniques is the key to further progress in automatic analysis and constant-propagation allows us to illustrate this point in a theoretical study.

After a general overview, the monograph consists of three essentially self-contained parts that can be read independently of each other. These parts study: a hierarchy of constants in sequential programs, inherent limits of flow analysis of parallel programs, and how to overcome these limits by abandoning a classic atomic execution assumption.

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Non-Fiction Mathematics Algebra Computing & I.T.Computer Programming & Software Development Software Engineering Programming & Scripting Languages Computer Science Computer Architecture & Logic Design Systems Analysis & Design

Introduction	p. 1
A Hierarchy of Constants	p. 13
A Taxonomy of Constants	p. 16
Flow Graphs	p. 16
May- and Must-Constants	p. 17
Weakened Constant Detection Problems	p. 19
Classes of Integer Constants	p. 21
Known Results	p. 22
New Undecidability Results	p. 24
New Intractability Results	p. 25
Summary	p. 29
Deciding Constants by Effective Weakest Preconditions	p. 31
Presburger and Polynomial Constants	p. 32
Presburger-Constant Detection at a Glance	p. 33
A Generic Algorithm	p. 37
Detection of Presburger Constants	p. 40
A Primer on Computable Ideal Theory	p. 43
More About Z[x₁,.,x_n]	p. 45
Z[x₁,.,x_n] as a Complete Lattice	p. 45
Zeros	p. 45
Substitution	p. 46
Projection	p. 46
Detection of Polynomial Constants	p. 47
Conclusion	p. 49
Limits of Parallel Flow Analysis	p. 53
A Motivating Example	p. 55
Parallel Programs	p. 56
Interprocedural Copy-Constant Detection	p. 57
Two-Counter Machines	p. 58
Constructing a Program	p. 59
Correctness of the Reduction	p. 62
Intraprocedural Copy-Constant Detection	p. 62
Copy-Constant Detection in Loop-Free Programs	p. 66
Beyond Fork/Join Parallelism	p. 67
Owicki/Gries-Style Program Proofs	p. 67
Correctness of the Reduction in Section 4.3	p. 68
Enriching the Program	p. 68
The Proof Outlines	p. 69
Interference Freedom	p. 72
Correctness of the Reduction in Section 4.4	p. 73
Enriching the Program	p. 73
An Auxiliary Predicate	p. 73
Proof Outline for p₀	p. 74
Proof Outline for p_i(r)	p. 75
Proof Outline for Main	p. 76
Interference Freedom	p. 77
Conclusion	p. 78
Parallel Flow Graphs	p. 81
Parallel Flow Graphs	p. 82
Operational Semantics	p. 84
Atomic Runs	p. 86
The Run Sets of Ultimate Interest	p. 87
The Constraint Systems	p. 88
Same-Level Runs	p. 88
Inverse Same-Level Runs	p. 90
Two Assumptions and a Simple Analysis	p. 91
Reaching Runs	p. 92
Terminating Runs	p. 94
Bridging Runs	p. 94
The General Case	p. 96
Discussion	p. 98
Non-atomic Execution	p. 101
Modeling Non-atomic Execution by Virtual Variables	p. 103
A Motivating Example	p. 105
The Domain of Non-atomic Run Sets	p. 106
Base Statements	p. 107
Sequential Composition	p. 108
Interleaving Operator	p. 108
Pre-operator	p. 109
Post-operator	p. 109
Conclusion	p. 109
Dependence Traces	p. 111
Transparency and Dependences	p. 113
Dependence Traces	p. 114
Implication Order	p. 116
Subsumption Order	p. 117
A Lattice of Antichains	p. 118
Short Dependence Traces	p. 121
The Abstract Domain	p. 124
Pre-operator	p. 126
Post-operator	p. 128
Sequential Composition	p. 128
Interleaving	p. 130
Complementary Dependence Traces	p. 131
Interleaving Operator	p. 132
Soundness Lemmas	p. 132
Completeness Lemmas	p. 136
Proof of Theorem 7.11.1	p. 139
Base Edges	p. 140
Running Time	p. 141
Discussion	p. 142
Detecting Copy Constants and Eliminating Faint Code	p. 145
Copy-Constant Detection	p. 146
Faint-Code Elimination	p. 148
Running Time	p. 150
Conclusion	p. 152
Complexity in the Non-atomic Scenario	p. 153
The SAT-reduction	p. 154
Towards Stronger Lower Bounds	p. 156
Assignment Statements That Propagate Twice	p. 157
Propagating Runs of Exponential Length	p. 159
Summary	p. 160
Conclusion	p. 161
Future Research	p. 163
A Primer on Constraint-Based Program Analysis	p. 165
References	p. 173
Table of Contents provided by Publisher. All Rights Reserved.

Variations on Constants

Flow Analysis of Sequential and Parallel Programs

At a Glance

Paperback

Shipping

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