Computational complexity theory
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Structural complexity theory
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Measures of complexity
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P = NP problem
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P versus NP problem
Complexity class
In computational complexity theory, a complexity class is a set of problems of related resource-based complexity. A typical complexity class has a definition of the form:For example, the class NP is t...
Reduction (complexity)
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Time hierarchy theorem
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Space hierarchy theorem
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Probabilistic complexity classes
Reduction (complexity)
In computability theory and computational complexity theory, a reduction is an algorithm for transforming one problem into another problem. A reduction from one problem to another may be used to show ...
Time hierarchy theorem
In computational complexity theory, the time hierarchy theorems are important statements about time-bounded computation on Turing machines. Informally, these theorems say that given more time, a Turin...
Space hierarchy theorem
In computational complexity theory, the space hierarchy theorems are separation results that show that both deterministic and nondeterministic machines can solve more problems in (asymptotically) more...
Probabilistic complexity classes
Arthur-Merlin protocol
In computational complexity theory, an Arthur–Merlin protocol is an interactive proof system in which the verifier's coin tosses are constrained to be public (i.e. known to the prover too). This...
MAX-2-SAT
In computer science, 2-satisfiability (abbreviated as 2-SAT or just 2SAT) is the problem of determining whether a collection of two-valued (Boolean or binary) variables with constraints on pairs of va...
AWPP (complexity)
In theoretical computer science, Almost Wide Probabilistic Polynomial-Time (AWPP) is a complexity class for problems in the context of quantum computing.AWPP contains the BQP (Bounded error, Quantum, ...
Minimum-weight triangulation
In computational geometry and computer science, the minimum-weight triangulation problem is the problem of finding a triangulation of minimal total edge length. That is, an input polygon or the convex...
IP (complexity)
In computational complexity theory, the class IP (which stands for Interactive Polynomial time) is the class of problems solvable by an interactive proof system. The concept of an interactive proof s...
IP (complexity) - Wikipedia
SNP (complexity)
In computational complexity theory, SNP (from Strict NP) is a complexity class containing a limited subset of NP based on its logical characterization in terms of graph-theoretical properties. It form...
FL (complexity)
In computational complexity theory, the complexity class FL is the set of function problems which can be solved by a deterministic Turing machine in a logarithmic amount of memory space. As in the def...
Polynomial-time approximation scheme
In computer science, a polynomial-time approximation scheme (PTAS) is a type of approximation algorithm for optimization problems (most often, NP-hard optimization problems).A PTAS is an algorithm whi...
UP (complexity)
In complexity theory, UP ("Unambiguous Non-deterministic Polynomial-time") is the complexity class of decision problems solvable in polynomial time on a non-deterministic Turing machine with at most o...
Sharp-P-complete
#P-complete, pronounced "sharp P complete" or "number P complete" is a complexity class in computational complexity theory. By definition, a problem is #P-complete if and only if it is in #P, and ever...
Co-NP
In computational complexity theory, co-NP is a complexity class. A decision problem is a member of co-NP if and only if its complement is in the complexity class NP. In simple terms, co-NP is the c...
Strongly NP-complete
In computational complexity, strong NP-completeness is a property of computational problems that is a special case of NP-completeness. A general computational problem may have numerical parameters. F...
DTIME
In computational complexity theory, DTIME (or TIME) is the computational resource of computation time for a deterministic Turing machine. It represents the amount of time (or number of computation st...
FNP (complexity)
In computational complexity theory, the complexity class FNP is the function problem extension of the decision problem class NP. The name is somewhat of a misnomer, since technically it is a class of ...
Set splitting problem
In computational complexity theory, the Set Splitting problem is the following decision problem: given a family F of subsets of a finite set S, decide whether there exists a partition of S into two su...
NC (complexity)
In complexity theory, the class NC (for "Nick's Class") is the set of decision problems decidable in polylogarithmic time on a parallel computer with a polynomial number of processors. In other words...
P-complete
In complexity theory, the notion of P-complete decision problems is useful in the analysis of both:Formally, a decision problem is P-complete (complete for the complexity class P) if it is in P and t...
S2P (complexity)
In computational complexity theory, SP2 is a complexity class, intermediate between the first and second levels of the polynomial hierarchy. A language is in if there exists a polynomial-time predic...
LH (complexity)
In computational complexity, the logarithmic time hierarchy (LH) is the complexity class of all computational problems solvable in a logarithmic amount of computation time on an alternating Turing mac...
P/poly
In computational complexity theory, P/poly is the complexity class of languages recognized by a polynomial-time Turing machine with a polynomial-bounded advice function. It is also equivalently defin...
Computational complexity of mathematical operations
The following tables list the running time of various algorithms for common mathematical operations.Here, complexity refers to the time complexity of performing computations on a multitape Turing mach...
GI (complexity)
The graph isomorphism problem is the computational problem of determining whether two finite graphs are isomorphic.Besides its practical importance, the graph isomorphism problem is a curiosity in com...
NE (complexity)
In computational complexity theory, the complexity class NE is the set of decision problems that can be solved by a non-deterministic Turing machine in time O(k) for some k.NE, unlike the similar clas...
EXPSPACE
In complexity theory, EXPSPACE is the set of all decision problems solvable by a deterministic Turing machine in O(2) space, where p(n) is a polynomial function of n. (Some authors restrict p(n) to b...
ELEMENTARY
In computational complexity theory, the complexity class ELEMENTARY of elementary recursive functions is the union of the classes in the exponential hierarchy.The name was coined by László Kalmár, in ...
P (complexity)
In computational complexity theory, P, also known as PTIME or DTIME(n), is one of the most fundamental complexity classes. It contains all decision problems that can be solved by a deterministic Turin...
P (complexity) - Wikipedia