Polynomial Invariants for Affine Programs
نویسندگان
چکیده
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. ACM Reference Format: Ehud Hrushovski, Joël Ouaknine, Amaury Pouly, and James Worrell. 2018. Polynomial Invariants for Affine Programs. In Proceedings of . ACM, New York, NY, USA, 9 pages. h ps://doi.org/10.1145/nnnnnnn.nnnnnnn
منابع مشابه
Image Recognition by Affine Tchebichef Moment Invariants
Tchebichef moments are successfully used in the field of image analysis because of their polynomial properties of discrete and orthogonal. In this paper, two new affine invariant sets are introduced for object recognition using discrete orthogonal Tchebichef moments. The current study constructs affine Tchebichef invariants by normalization method. Firstly, image is normalized to a standard for...
متن کاملGenerating Loop Invariants by Computing Vanishing Ideals of Sample Points
Loop invariants play a very important role in proving correctness of programs. In this paper, we address the problem of generating invariants of polynomial loop programs. We present a new approach, for generating polynomial equation invariants of polynomial loop programs through computing vanishing ideals of sample points. We apply rational function interpolation, based on early termination tec...
متن کاملComputation of polytopic invariants for polynomial dynamical systems using linear programming
This paper deals with the computation of polytopic invariant sets for polynomial dynamical systems. An invariant set of a dynamical system is a subset of the state space such that if the state of the system belongs to the set at a given instant, it will remain in the set forever in the future. Polytopic invariants for polynomial systems can be verified by solving a set of optimization problems ...
متن کاملAffine Invariant 3L Fitting of Implicit Polynomials
Combining implicit polynomials and algebraic invariants for representing and recognizing complicated objects proves to be a powerful technique. However, a basic requirement for using implicit polynomials for affine invariant recognition is to have an affine invariant fitting algorithm. In this paper, we study the problem of affine invariant fitting of an implicit polynomial to data. Received Ja...
متن کاملExtended affine Weyl groups and Frobenius manifolds
We define certain extensions of affine Weyl groups (distinct from these considered by K. Saito [S1] in the theory of extended affine root systems), prove an analogue of Chevalley theorem for their invariants, and construct a Frobenius structure on their orbit spaces. This produces solutions F (t1, . . . , tn) of WDVV equations of associativity polynomial in t1, . . . , tn−1, exp tn.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/1802.01810 شماره
صفحات -
تاریخ انتشار 2018