Polynomial Invariants for Affine Programs
Polynomial Invariants for Affine Programs
复制标题
DOI：
10.1145/3209108.3209142
复制
发表时间：
2018-02
期刊：
影响因子：
--
通讯作者：
E. Hrushovski;Joël Ouaknine;Amaury Pouly;J. Worrell
中科院分区：
文献类型：
--
作者：
E. Hrushovski;Joël Ouaknine;Amaury Pouly;J. Worrell
我们展示了一种算法来计算在给定仿射程序的每个位置处保持的最强多项式（或代数）不变量（即，只有非确定性（与条件相反）分支的程序，其所有赋值都由仿射表达式给出）。我们的主要工具是一个代数结果的独立利益：给定一组有限的理性方阵相同的尺寸，我们展示了如何计算Zebriki封闭的半群，他们产生。
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.