Undecidability of Network Coding, Conditional Information Inequalities, and Conditional Independence Implication
Cheuk Ting Li
Abstract
We resolve three long-standing open problems, namely the (algorithmic) decidability of network coding, the decidability of conditional information inequalities, and the decidability of conditional independence implication among random variables, by showing that these problems are undecidable. The proof utilizes a construction inspired by Herrmann’s arguments on embedded multivalued database dependencies, a network studied by Dougherty, Freiling and Zeger, together with a novel construction to represent group automorphisms on top of the network.
Topics & Concepts
Undecidable problemDecidabilityConditional independenceMathematicsTheoretical computer scienceConditional expectationDiscrete mathematicsConditional probabilityIndependence (probability theory)Computer scienceEconometricsStatisticsCooperative Communication and Network CodingWireless Communication Security TechniquesCryptography and Data Security