14-time-complexity

# 14-time-complexity - Complexity Theory Up to now we...

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Complexity Theory Up to now we investigated whether a problem is in principle solvable algorithmically, that is, we asked the question whether a particular language is, Decidable: machine halts on all inputs (total computable functions) Turing-Recognizable: machine loops forever on some inputs (partially computable functions) However, we did not investigate the cost of the computation itself - the amount of resources the computation absorbs (time, space, etc. ) In the following we discuss time complexity and space complexity . Furthermore, we assume that we are dealing with total computable functions, that is, the respective language is decidable. – p. 1/

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Time Complexity Definition: Let M be a deterministic TM that halts on all inputs. The running time or time complexity of M is the function f : N N , where f ( n ) is the maximum number of steps that M uses on any input of length n . If f ( n ) is the running time of M , then we say that M runs in time f ( n ) and that M is an f ( n ) time TM. Customarily we use n to represent the length of the input.
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