search problem
If is a binary relation such that and is a Turing machine, then calculates if:
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If is such that there is some such that then accepts with output such that (there may be multiple , and need only find one of them)
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If is such that there is no such that then rejects
Note that the of a partial function is a binary relation, and if calculates a partial function then there is at most one possible output.
A can be viewed as a search problem, and a Turing machine which calculates is also said to solve it. Every search problem has a corresponding decision problem, namely .
This definition may be generalized to -ary relations using any suitable encoding which allows multiple strings to be compressed into one string (for instance by listing them consecutively with a delimiter).
Title | search problem |
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Canonical name | SearchProblem |
Date of creation | 2013-03-22 13:01:39 |
Last modified on | 2013-03-22 13:01:39 |
Owner | Henry (455) |
Last modified by | Henry (455) |
Numerical id | 7 |
Author | Henry (455) |
Entry type | Definition |
Classification | msc 68Q25 |
Defines | calculate |