English

Polynomial Invariants for Affine Programs

Logic in Computer Science 2018-05-03 v2 Discrete Mathematics Algebraic Geometry

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.

Keywords

Cite

@article{arxiv.1802.01810,
  title  = {Polynomial Invariants for Affine Programs},
  author = {Ehud Hrushovski and Joël Ouaknine and Amaury Pouly and James Worrell},
  journal= {arXiv preprint arXiv:1802.01810},
  year   = {2018}
}
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