# Difference between deterministic and nondeterministic universal turing machine

It is known that a nondeterministic universal turing machine (UTM) can simulate another nondeterministic TM with running time $t(n)$ in time $c t(n)$, where $c$ is a constant. It is also known that a deterministic UTM can simulate another deterministic TM with running time $t(n)$ in time $t(n)\log(t(n))$.

My question is: why is there a $\log(t(n))$ slowdown in the simulation of a deterministic TM by a UTM, as opposed to a constant factor slowdown in the nondeterministic case?

• Have you tried looking at the proofs of these simulations? If what you're stating is correct, then some trick that works for nondeterministic machines doesn't work for deterministic ones. – Yuval Filmus Feb 23 '14 at 19:10