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Functional behavior of nondeterministic programs

  • Michael G. Main
  • David B. Benson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 158)

Abstract

The functional behavior of a deterministic program is a function f:D→D, where D is some set of states for the computation. This notion of functional behaviors can be extended to nondeterministic programs using techniques from linear algebra. In particular, the functional behavior of a nondeterministic program is a linear transformation f:A→A, where A is a free semiring module. Other notions from linear algebra carry over into this setting. For example, weakest preconditions and predicate transformers correspond to well-studied concepts in linear algebra. Finally, we consider multiple-input and multiple-output programs. The functional behavior of a nondeterministic program with multiple inputs and outputs is a linear transformation f:⊗ m A→⊗ n A, where ⊗ x A is an iterated tensor product of the semiring module A. This is in contrast to the deterministic case, where such a program is a function f:D m →D n , using the Cartesian products D m and D n .

Keywords

Tensor Product Linear Transformation Functional Behavior Deterministic State Commutative Monoid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • Michael G. Main
    • 1
  • David B. Benson
    • 2
  1. 1.Department of Computer ScienceUniversity of ColoradoBoulderUSA
  2. 2.Department of Computer ScienceWashington State UniversityPullman

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