# Limits on the time of computation for a UTM simulating a TM

According to source page 20, theorem 1.9, it states that there is a universal Turing machine that can simulate any Turing machine with a time overhead of $O(\log n)$.

Can a universal Turing machine exists with less overhead? Can we prove that no such universal Turing machine exists?

If not, can we at least prove a lower bound on the overhead?

• I believe it is an open question. – Yuval Filmus Apr 6 '17 at 18:27
• @Yuval What about if we restrict a UTM to simulating another UTM. Is it then still an open question? – Anon21 Apr 6 '17 at 18:30
• This isn't really well-defined. – Yuval Filmus Apr 6 '17 at 18:30
• related – Ariel May 2 '18 at 7:15