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.
This work was supported in part by National Science Foundation Grant MCS-8003433.
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Main, M.G., Benson, D.B. (1983). Functional behavior of nondeterministic programs. In: Karpinski, M. (eds) Foundations of Computation Theory. FCT 1983. Lecture Notes in Computer Science, vol 158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12689-9_112
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DOI: https://doi.org/10.1007/3-540-12689-9_112
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