Authors: Arley Gomez; Carolina Mejia; J. Andres Montoya
Addresses: Instituto de matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia ' Instituto de matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia ' Instituto de matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia
Abstract: We study the definability of the almost-entropic regions by finite lists of algebraic inequalities. First, we study linear information inequalities and polyhedrality, we present a proof of a theorem of Matus, which claims that the almost-entropic regions are not polyhedral. Then, we study polynomial inequalities and semialgebraicity, we show that the semialgebracity of the almost-entropic regions is something that depends on the essentially conditionality of a certain class of conditional information inequalities. Those results suggest that the almost-entropic regions are not semialgebraic. We conjecture that those regions are not decidable.
Keywords: entropic regions; entropic vectors; entropy; information inequalities; polyhedrality; Shannon inequalities; algebraic inequalities; polynomial inequalities; semialgebraicity.
International Journal of Information and Coding Theory, 2017 Vol.4 No.1, pp.1 - 18
Received: 11 Apr 2016
Accepted: 01 Aug 2016
Published online: 02 Jan 2017 *