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NTIME
In computational complexity theory, the complexity class NTIME(''f''(''n'')) is the set of decision problems that can be solved by a non-deterministic Turing machine which runs in time ''O''(''f''(''n'')). Here ''O'' is the big O notation, ''f'' is some function, and ''n'' is the size of the input (for which the problem is to be decided). Meaning This means that there is a non-deterministic machine which, for a given input of size ''n'', will run in time ''O''(''f''(''n'')) (i.e. within a constant multiple of ''f''(''n''), for ''n'' greater than some value), and will always "reject" the input if the answer to the decision problem is "no" for that input, while if the answer is "yes" the machine will "accept" that input for at least one computation path. Equivalently, there is a deterministic Turing machine ''M'' that runs in time ''O''(''f''(''n'')) and is able to check an ''O''(''f''(''n''))-length certificate for an input; if the input is a "yes" instance, then at least one certifi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time Hierarchy Theorem
In computational complexity theory, the time hierarchy theorems are important statements about time-bounded computation on Turing machines. Informally, these theorems say that given more time, a Turing machine can solve more problems. For example, there are problems that can be solved with ''n''2 time but not ''n'' time. The time hierarchy theorem for deterministic multi-tape Turing machines was first proven by Richard E. Stearns and Juris Hartmanis in 1965. It was improved a year later when F. C. Hennie and Richard E. Stearns improved the efficiency of the Universal Turing machine. Consequent to the theorem, for every deterministic time-bounded complexity class, there is a strictly larger time-bounded complexity class, and so the time-bounded hierarchy of complexity classes does not completely collapse. More precisely, the time hierarchy theorem for deterministic Turing machines states that for all time-constructible functions ''f''(''n''), :\mathsf\left(o\left(\frac\right)\righ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |