article

Affine relationships among variables of a program

Author:

Michael KarrAuthors Info & Claims

Acta Informatica, Volume 6, Issue 2

Pages 133 - 151

https://doi.org/10.1007/BF00268497

Published: 01 June 1976 Publication History

Abstract

Several optimizations of programs can be performed when in certain regions of a program equality relationships hold between a linear combination of the variables of the program and a constant. This paper presents a practical approach to detecting these relationships by considering the problem from the viewpoint of linear algebra. Key to the practicality of this approach is an algorithm for the calculation of the "sum" of linear subspaces.

References

[1]

MacLane, S., Birkhoff, G.: Algebra. New York: MacMillan 1967

Google Scholar

[2]

Munkres, J. R.: Elementary linear algebra. Reading (Mass.): Addison-Wesley 1964

Google Scholar

[3]

Floyd, R.: Assigning meanings to programs. In: Schwartz, J. (ed.): Mathematical aspects of computer science 19. Providence (R.I.): American Mathematical Society 1967, p. 19---32

Google Scholar

[4]

Wegbreit, Ben: Property extraction in well-Founded property sets. Center for Research in Computing Technology, Harvard University, Cambridge (Mass.) and Computer Science Division, Bolt, Beranek, and Newman, Inc., Cambridge (Mass.), February 1973

Google Scholar

[5]

Karr, M.: Gathering information about Programs. Massachusetts Computer Associates, Inc., (In preparation)

Google Scholar

[6]

Birkhoff, G.: Lattice theory. Colloquium Publication XXV, 3. Ed., Providence (R.I.): American Mathematical Society 1973

Google Scholar

Cited By

View all

Bayarmagnai EMohammadi FPrébet R(2024)Algebraic Tools for Computing Polynomial Loop InvariantsProceedings of the 2024 International Symposium on Symbolic and Algebraic Computation10.1145/3666000.3669710(371-381)Online publication date: 16-Jul-2024
https://dl.acm.org/doi/10.1145/3666000.3669710
Ciobanu LZetzsche GSobocinski PLago UEsparza J(2024)Slice closures of indexed languages and word equations with counting constraintsProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662134(1-12)Online publication date: 8-Jul-2024
https://dl.acm.org/doi/10.1145/3661814.3662134
Nguyen HPriyadarshan SSekar RChristakis MPradel M(2024)Scalable, Sound, and Accurate Jump Table AnalysisProceedings of the 33rd ACM SIGSOFT International Symposium on Software Testing and Analysis10.1145/3650212.3680301(541-552)Online publication date: 11-Sep-2024
https://dl.acm.org/doi/10.1145/3650212.3680301
Show More Cited By

Recommendations

Causal Relationships amongst Sensors in the Trinity Supercomputer: work in progress
MLCS'18: Proceedings of the First Workshop on Machine Learning for Computing Systems

HPC systems are inherently complex, both to work with and to maintain. Trying to anticipate a sudden event, such as component failure or how the system will react to a newly installed module, is too large and convoluted of a problem for a single person ...
Harmonic Relationships Among Random Variables

The approximate probability that m random variables out of a set of n uniformly and independently distributed on $(a,b)$ are harmonically related to within a tolerance of $100t\% $ has been calculated. The results indicate the need for accuracy in ...
Relationships between and among models
Proceedings of the workshop on Data abstraction, databases and conceptual modelling

Mylopoulos: When we talk about a model, it can be either a program snapshot or execution, or a program, a data base, a conceptual schema, or a knowledge base. We can think of a program as consisting of units of some sort, e.g., procedures, assertions, ...

Comments

Information & Contributors

Information

Published In

Acta Informatica Volume 6, Issue 2

June 1976

97 pages

ISSN:0001-5903

Issue’s Table of Contents

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 June 1976

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

140
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 21 Sep 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Bayarmagnai EMohammadi FPrébet R(2024)Algebraic Tools for Computing Polynomial Loop InvariantsProceedings of the 2024 International Symposium on Symbolic and Algebraic Computation10.1145/3666000.3669710(371-381)Online publication date: 16-Jul-2024
https://dl.acm.org/doi/10.1145/3666000.3669710
Ciobanu LZetzsche GSobocinski PLago UEsparza J(2024)Slice closures of indexed languages and word equations with counting constraintsProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662134(1-12)Online publication date: 8-Jul-2024
https://dl.acm.org/doi/10.1145/3661814.3662134
Nguyen HPriyadarshan SSekar RChristakis MPradel M(2024)Scalable, Sound, and Accurate Jump Table AnalysisProceedings of the 33rd ACM SIGSOFT International Symposium on Software Testing and Analysis10.1145/3650212.3680301(541-552)Online publication date: 11-Sep-2024
https://dl.acm.org/doi/10.1145/3650212.3680301
Zhao JXu JDi PNie WHu JYi YYang SGeng ZZhang RLi BGan ZJin X(2024)Modeling the Interplay between Loop Tiling and Fusion in Optimizing Compilers Using Affine RelationsACM Transactions on Computer Systems10.1145/363530541:1-4(1-45)Online publication date: 15-Jan-2024
https://dl.acm.org/doi/10.1145/3635305
Müllner JMoosbrugger MKovács L(2024)Strong Invariants Are Hard: On the Hardness of Strongest Polynomial Invariants for (Probabilistic) ProgramsProceedings of the ACM on Programming Languages10.1145/36328728:POPL(882-910)Online publication date: 5-Jan-2024
https://dl.acm.org/doi/10.1145/3632872
Cousot P(2024)Calculational Design of [In]Correctness Transformational Program Logics by Abstract InterpretationProceedings of the ACM on Programming Languages10.1145/36328498:POPL(175-208)Online publication date: 5-Jan-2024
https://dl.acm.org/doi/10.1145/3632849
Seidl HErhard JTilscher SSchwarz M(2024)Non-numerical weakly relational domainsInternational Journal on Software Tools for Technology Transfer (STTT)10.1007/s10009-024-00755-026:4(479-494)Online publication date: 1-Aug-2024
https://dl.acm.org/doi/10.1007/s10009-024-00755-0
Ghardallou WMohammadi HLinger RPleszkoch MLoh JMili A(2024)Invariant relations for affine loopsActa Informatica10.1007/s00236-024-00457-961:3(261-314)Online publication date: 1-Sep-2024
https://dl.acm.org/doi/10.1007/s00236-024-00457-9
Hrushovski EOuaknine JPouly AWorrell J(2023)On Strongest Algebraic Program InvariantsJournal of the ACM10.1145/361431970:5(1-22)Online publication date: 11-Oct-2023
https://dl.acm.org/doi/10.1145/3614319
Yu SWang TWang JJust RFraser G(2023)Loop Invariant Inference through SMT Solving Enhanced Reinforcement LearningProceedings of the 32nd ACM SIGSOFT International Symposium on Software Testing and Analysis10.1145/3597926.3598047(175-187)Online publication date: 12-Jul-2023
https://dl.acm.org/doi/10.1145/3597926.3598047
Show More Cited By

View Options

View options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Abstract

References

Cited By

Recommendations

Causal Relationships amongst Sensors in the Trinity Supercomputer: work in progress

Harmonic Relationships Among Random Variables

Relationships between and among models

Comments

Information

Published In

Publisher

Publication History

Qualifiers

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

Get Access

Login options

Full Access

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations