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Separate nondeterministic and deterministic linear time in general models

Establish that NTIME[n] ≠ TIME[n] for computational models beyond one-dimensional multitape Turing machines, such as more general or random-access models.

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Background

Paul, Pippenger, Szemerédi, and Trotter proved NTIME[n] ≠ TIME[n] for (one-dimensional) multitape Turing machines, a landmark result.

Extending this separation to more general models has remained notoriously difficult, and the authors explicitly note that the problem is still open.

References

Unfortunately, their proof only works for (one-dimensional) multitape Turing machines, and it is infamously still open to prove $\NTIME[n] \neq \TIME[n]$ in more general models.

— Simulating Time With Square-Root Space (2502.17779 - Williams, 25 Feb 2025) in Section 2, More Related Work