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arXiv · 1802.01810

Polynomial Invariants for Affine Programs

Ehud Hrushovski·Joël Ouaknine·Amaury Pouly·James Worrell
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Abstract

We exhibit an algorithm to compute the strongest polynomial (or algebraic) invariants that hold at each location of a given affine program (i.e., a program having only non-deterministic (as opposed to conditional) branching and all of whose assignments are given by affine expressions). Our main tool is an algebraic result of independent interest: given a finite set of rational square matrices of the same dimension, we show how to compute the Zariski closure of the semigroup that they generate.

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Ehud Hrushovski, Joël Ouaknine, Amaury Pouly, James Worrell. 2018-02-06. Polynomial Invariants for Affine Programs. https://arxiv.org/abs/1802.01810

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