Polynomial invariants for affine programs

Ehud Hrushovski, Joël Ouaknine, Amaury Pouly, and James Worrell

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.

Proceedings of LICS 18, 2018. 10 pages.

PDF © 2018 Association for Computing Machinery.

Imprint / Data Protection