January 2011
Intermediate to advanced
192 pages
5h 34m
English
Content preview from Computability Theory
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7 Polynomial-Time Computability
7.1 Feasible Computability
Up to now, we have approached computability from the point of view that there should
be no constraints either on the time required for a particular computation or on the
amount of memory space that might be required. The result is that some total com-
putable functions will take a very long time to compute. If a function f grows very
rapidly, then for large x, it will take a long time simply to generate the output f (x). But
there are also bounded functions that require a large amount of time.
In this chapter,
1
we want to adopt a different attitude, and we want to pay some
attention to the running time that a program might require. For the most part, we
will not attempt to give complete rigorous ...
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