decision problem
Let be a Turing machine and let be a language. We say decides if for any , accepts , and for any , rejects .
We say enumerates if:
For some Turing machines (for instance non-deterministic machines) these definitions are equivalent, but for others they are not. For example, in order for a deterministic Turing machine to decide , it must be that halts on every input. On the other hand could enumerate if it does not halt on some strings which are not in .
is sometimes said to be a decision problem, and a Turing machine which decides it is said to solve the decision problem.
The set of strings which accepts is denoted .
Title | decision problem |
---|---|
Canonical name | DecisionProblem |
Date of creation | 2013-03-22 13:01:33 |
Last modified on | 2013-03-22 13:01:33 |
Owner | Henry (455) |
Last modified by | Henry (455) |
Numerical id | 12 |
Author | Henry (455) |
Entry type | Definition |
Classification | msc 68Q25 |
Defines | enumerates |
Defines | decide |