Examples of using Complexity classes in English and their translations into Serbian
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Important complexity classes.
Many complexity classes can be characterized in terms of the mathematical logic needed to express them; see descriptive complexity. .
Relationships between complexity classes.
Simpler complexity classes are defined by the following factors.
But bounding the computation time above by some concrete function f(n)often yields complexity classes that depend on the chosen machine model.
Many complexity classes are defined using the concept of a reduction.
Purpose bounding the computation time by Above Some concrete function f( n)Often yields complexity classes That depends on the Machine Chosen model.
Several important complexity classes are defined in terms of DSPACE.
P(complexity) In computational complexity theory, P, also known as PTIME or DTIME(nO(1)),is one of the most fundamental complexity classes.
Several important complexity classes can be defined in terms of NSPACE.
Polynomial-time reductions are frequently used in complexity theory for defining both complexity classes and complete problems for those classes. .
Several important space complexity classes are sublinear, that is, smaller than the size of the input.
Counting techniques(rule of sum and product, inclusion-exclusion principle, generating functions);computational complexity theory(basic concepts and complexity classes); applications in cryptography(symmetric and asymmetric cryptography systems).
The relationship between the complexity classes P and NP is an unsolved question in theoretical computer science.
Simpler complexity classes are defined by the following factors: The type of computational problem: The most commonly used problems are decision problems.
Polynomial-time many-one reductions have been used to define complete problems for other complexity classes, including the PSPACE-complete languages and EXPTIME-complete languages.
Many important complexity classes can be defined by bounding the time or space used by the algorithm.
The model of computation: The most common model of computation is the deterministic Turing machine, but many complexity classes are based on non-deterministic Turing machines, Boolean circuits, quantum Turing machines, monotone circuits, etc.
Other important complexity classes include BPP, ZPP and RP, which are defined using probabilistic Turing machines.
The Blum axioms can be used to define complexity classes without referring to a concrete computational model.
For the complexity classes defined in this way, it is desirable to prove that relaxing the requirements on(say) computation time indeed defines a bigger set of problems.
One possible route to separating two complexity classes is to find some closure property possessed by one and not by the other.
However, complexity classes can be defined based on function problems(an example is FP), counting problems(e.g. P), optimization problems, promise problems, etc.
Oracle machines are useful for investigating the relationship between complexity classes P and NP, by considering the relationship between PA and NPA for an oracle A. In particular, it has been shown there exist languages A and B such that PA=NPA and PB≠NPB(Baker, Gill, and Solovay 1975).
Provided that the complexity classes P and NP are not equal, neither 2-, nor Horn-, nor XOR-satisfiability is NP-complete, unlike SAT.
The relation between the complexity classes P and NP is studied in computational complexity theory, the part of the theory of computation dealing with the resources required during computation to solve a given problem.
Therefore, for complexity classes within P such as L, NL, NC, and P itself, polynomial-time reductions cannot be used to define complete languages: if they were used in this way, every nontrivial problem in P would be complete.
This motivates the concept of a problem being hard for a complexity class.
The complexity class NP can be defined in terms of NTIME as.
However, in some cases a complexity class may be defined by reductions.