Linear-Time Multitape Turing Machine Multiplication

Determine whether there exists a multitape Turing machine that multiplies two n-bit integers in O(n) time and correctly solves MULT_n on all n-bit inputs.

Background

The paper uses integer multiplication as a motivational example to illustrate rare-case hardness. It cites the result that multiplying two n-bit integers is solvable in O(n log n) time on a multitape Turing machine, and frames the open question of whether truly linear time is achievable on this classical model. Resolving this would clarify time complexity limits for basic arithmetic on multitape Turing machines and illuminate the gap between currently known near-linear algorithms and potential linear-time algorithms.