Download - Lecture 22. Time of DTM
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Lecture 22. Time of DTM
Time 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.
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Complexity 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 Up
Suppose t(n)/n → infinity as n → infinity. Then for any constant c > 0,
DTIME(t(n)) = DTIME(ct(n))