# Alternating Turing Machine: Why one cannot generalize the proof of AL = P?

In their paper "Alternation" Chandra et al. show how an Alternating Turing Machine can simulate a Deterministic Turing Machine with time-complexity $t(n)$ using only $\log(t(n))$ space what implies $P \subseteq AL$.

I wonder why one cannot use the same (or at least a quite similar) construction in order to simulate a Non-deterministic Turing machine with time complexity $t(n)$ using only $\log(t(n))$ space.

• Possibly, a word "monotone" influences. – rus9384 Sep 29 '17 at 1:19
• Have you read the paper? The proof requires $\log t(n)$ alternations. Only one alternation won't do. – Yuval Filmus Sep 29 '17 at 6:44