Decidability of max-plus comparison for three through 552 states

Determine whether exact comparison of max-plus automata is decidable for state bounds between three and 552 states, thereby resolving the portion of the bounded-state range not settled by the two-state result or the known 553-state undecidability theorem.

Background

Daviaud, Guillon, and Merlet established undecidability of exact comparison for max-plus automata with a fixed bound of 553 states and identified the range from 2 to 552 states as unresolved. The paper settles the two-state endpoint by proving decidability when the right-hand automaton has at most two states, including the stronger case of an arbitrary left-hand automaton.

Consequently, the state bounds from three through 552 remain the unresolved portion of the previously identified interval. The paper does not claim a result for those bounds; its contribution is specifically the two-state endpoint.