论常量变差

出版时间：2006-12  出版社：Springer-Verlag New York Inc  作者：Muller-Olm, Markus  页数：177  

内容概要

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.

书籍目录

1.  Introduction2.  A Hierarchy of Constants  2.1  A Taxonomy of Constants    2.1.1  Flow Graphs    2.1.2  May- and Must-Constants    2.1.3  Weakened Constant Detection Problems    2.1.4  Classes of Integer Constants  2.2  Known Results  2.3  New Undecidability Results  2.4  New Intractability Results  2.5  Summary3.  Deciding Constants by Effective Weakest Preconditions..  3.1  Presburger and Polynomial Constants  3.2  Presburger-Constant Detection at a Glance  3.3  A Generic Algorithm  3.4  Detection of Presburger Constants  3.5  A Primer on Computable Ideal Theory  3.6  More About Z[x1,...,xn]    3.6.1  Z[X1,...,Xn] as a Complete Lattice    3.6.2  Zeros    3.6.3  Substitution    3.6.4  Projection  3.7  Detection of Polynomial Constants  3.8  Conclusion4.  Limits of Parallel Flow Analysis  4.1  A Motivating Example  4.2  Parallel Programs  4.3  Interprocedural Copy-Constant Detection    4.3.1  Two-Counter Machines    4.3.2  Constructing a Program    4.3.3  Correctness of the Reduction  4.4  Intraprocedural Copy-Constant Detection  4.5  Copy-Constant Detection in Loop-Free Programs  4.6  Beyond Fork/Join Parallelism  4.7  Owicki/Gries-Style Program Proofs  4.8  Correctness of the Reduction in Section 4.3    4.8.1  Enriching the Program    4.8.2  The Proof Outlines    4.8.3  Interference Freedom  4.9  Correctness of the Reduction in Section 4.4    4.9.1  Enriching the Program    4.9.2  An Auxiliary Predicate    4.9.3  Proof Outline for 7r0    4.9.4  Proof Outline for 7ri(r)    4.9.5  Proof Outline for Main    4.9.6  Interference Freedom  4.10 Conclusion5.  Parallel Flow Graphs   5.1  Parallel Flow Graphs   5.2  Operational Semantics   5.3  Atomic Runs   5.4  The Run Sets of Ultimate Interest   5.5  The Constraint Systems      5.5.1  Same-Level Runs      5.5.2  Inverse Same-Level Runs      5.5.3  Two Assumptions and a Simple Analysis      5.5.4  Reaching Runs      5.5.5  Terminating Runs      5.5.6  Bridging Runs      5.5.7  The General Case   5.6  Discussion6.  Non-atomic Execution   6.1  Modeling Non-atomic Execution by Virtual Variables ...   6.2  A Motivating Example   6.3  The Domain of Non-atomic Run Sets     6.3.1  Base Statements     6.3.2  Sequential Composition     6.3.3  Interleaving Operator     6.3.4  Pre-operator     6.3.5  Post-operator  6.4  Conclusion  ……7.  Dependence Traces8.  Detecting Copy Constants and Eliminating Faint Code9.  Complexity in the Non-atomic Scenario10.  ConclusionA. A Primer on Constraint-Based Program AnalysisReferences