Lecture 22. Time of DTMTime of DTMTime BoundTheoremComplexity ClassModelLinear Speed UpLecture 22. Time of DTMTime of DTM•TimeM (x) = # of moves that DTM M takes on input x.•TimeM(x) < infinity iff x ε L(M).Time Bound M is said to have a time bound t(n) if for every x with |x| < n, TimeM(x) < max {n+1, t(n)}Theorem•For any multitape DTM M, there exists a one-tape DTM M’ to simulate M within time TimeM’(x) < c + (TimeM(x)) c is a constant.2Complexity Class•A language L has a (deterministic) time-complexity t(n) if there is a multitape DTM M accepting L, with time bound t(n).•DTIME(t(n)) = {L | L has a time bound t(n)}Model •Multitape TM with write-only output.Linear Speed UpSuppose t(n)/n → infinity as n → infinity. Then for any constant c > 0, DTIME(t(n)) =