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Counterexamples to the Markovity Conjecture for the Two-Receiver Broadcast Channel · arXivDesk

2608.13170Aug 13, 2026

Counterexamples to the Markovity Conjecture for the Two-Receiver Broadcast Channel

Yanxiao Liu, Mian Huang

Abstract

We present two counterexamples to the Markovity Conjecture of Gohari, Liu and Nair (ISIT 2025), which is a structural conjecture concerning the optimizers of the dual functional associated with Marton's inner bound and, if true, would greatly simplify the evaluation of Marton's inner bound. Both counterexamples are ternary-input broadcast channels with strictly positive transition probabilities and use the same nonrectangular $2\times2$ auxiliary structure. In each case, we exhibit an explicit non-Markov construction whose objective value is rigorously larger than that achievable by any construction satisfying the conjectured Markov structure. Both examples are obtained with the assistance of GPT-5.6 Sol and disprove the Markovity Conjecture.

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The paper addresses: Counterexamples to the Markovity Conjecture for the Two-Receiver Broadcast Channel.
We present two counterexamples to the Markovity Conjecture of Gohari, Liu and Nair (ISIT 2025), which is a structural conjecture concerning the optimizers of the dual functional associated with Marton's inner bound and, if true, would greatly simplify the evaluation of Marton's inner bound.