Acta Informatica

, Volume 6, Issue 2, pp 133–151 | Cite as

Affine relationships among variables of a program

  • Michael Karr
Article

Summary

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.

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References

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    Floyd, R.: Assigning meanings to programs. In: Schwartz, J. (ed.): Mathematical aspects of computer science 19. Providence (R.I.): American Mathematical Society 1967, p. 19–32Google Scholar
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    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 1973Google Scholar
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    Karr, M.: Gathering information about Programs. Massachusetts Computer Associates, Inc., (In preparation)Google Scholar
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    Birkhoff, G.: Lattice theory. Colloquium Publication XXV, 3. Ed., Providence (R.I.): American Mathematical Society 1973Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • Michael Karr
    • 1
  1. 1.Massachusetts Computer Associates Inc.Lakeside Office Park WakefieldUSA

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