On Convexity of Right-Closed Integral Sets
Journal Title: Journal of Advances in Mathematics and Computer Science - Year 2017, Vol 20, Issue 1
Abstract
Let N denote the set of non-negative integers. A set of non-negative, n-dimensional integral vectors, M⊂ Nn, is said to be right-closed, if ((x ∈M) ∧ (y ≥ x) ∧ (y ∈ Nn)) ⇒ (y ∈M). In this paper, we present a polynomial time algorithm for testing the convexity of a right-closed set of integral vectors, when the dimension n is xed. Right-closed set of integral vectors are in nitely large, by de nition. We compute the convex-hull of an appropriately-de ned nite subset of this in nite-set of vectors. We then check if a stylized Linear Program has a non-zero optimal value for a special collection of facets of this convex-hull. This result is to be viewed against the backdrop of the fact that checking the convexity of a real-valued, geometric set can only be accomplished in an approximate sense; and, the fact that most algorithms involving sets of real-valued vectors do not apply directly to their integral counterparts. This observation plays an important role in the ecient synthesis of Supervisory Policies that avoid Livelocks in Discrete-Event/Discrete-State Systems.
Authors and Affiliations
E. Salimi, R. S. Sreenivas
Keywords
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- EP ID EP321907
- DOI 10.9734/BJMCS/2017/30348
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