P (complexity class)
In complexity theory , P (also: PTIME ) is the complexity class that contains all decision problems that can be solved in polynomial time for deterministic Turing machines . This class of problems is generally considered to be the class of "practically solvable" problems.
A generalization of P is the class NP . The problems from NP can also be decided in polynomial time, but a non-realizable, namely nondeterministic machine model is used for this. P is certainly a subset of NP. However, one of the most important unsolved questions in theoretical computer science is whether P = NP holds ( see also P-NP problem ).
P is closed with a complement.
Relationship to other complexity classes
The following relationships are known:
- P EXPTIME
P-completeness
A decision problem is called P-full if and only if it is in the complexity class is P and when any problem in P by a calculation with logarithmic space consumption to be reduced, that is, if each of these reductions in the complexity class L is ( see also: completeness in complexity theory ).
A well-known P-complete problem is the circuit value problem , the purpose of which is to determine whether the result of a Boolean circuit given an input corresponds to a given output. These problems belong to the most difficult, still efficiently solvable problems from the complexity class P. P-complete problems are (at the moment) difficult to parallelize.
Known issues in P
A great many problems lie in P, which is generally not particularly noticed; As a rule, a suitable algorithm is then also known (such as the sorting problem with e.g. quicksort , runtime , etc.).
- PRIMES is a problem that, contrary to many earlier assumptions, is in P ( AKS prime number test , 2002)
P-complete problems
Web links
- P . In: Complexity Zoo. (English)
- A Compendium of problem Complete for P (English)