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28 relations: Adjacency matrix, Algorithm, Big O notation, Cambridge University Press, Christos Papadimitriou, Complexity class, Computational complexity theory, Decision problem, E (complexity), EXPTIME, Formal language, Game complexity, Hamiltonian path, Interactive proof system, Mihalis Yannakakis, NE (complexity), Non-deterministic Turing machine, NP (complexity), NP-completeness, NTIME, P (complexity), P versus NP problem, Padding argument, Polynomial-time reduction, Probabilistically checkable proof, Sparse language, Time complexity, Time hierarchy theorem.
Adjacency matrix
In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph.
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Algorithm
In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.
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Big O notation
Big O notation is a mathematical notation that describes the limiting behaviour of a function when the argument tends towards a particular value or infinity.
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Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
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Christos Papadimitriou
Christos Harilaos Papadimitriou (Greek: Χρήστος Χαρίλαος Παπαδημητρίου; born August 16, 1949) is a Greek theoretical computer scientist, and professor of Computer Science at Columbia University.
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Complexity class
In computational complexity theory, a complexity class is a set of problems of related resource-based complexity.
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Computational complexity theory
Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.
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Decision problem
In computability theory and computational complexity theory, a decision problem is a problem that can be posed as a yes-no question of the input values.
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E (complexity)
In computational complexity theory, the complexity class E is the set of decision problems that can be solved by a deterministic Turing machine in time 2O(n) and is therefore equal to the complexity class DTIME(2O(n)).
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EXPTIME
In computational complexity theory, the complexity class EXPTIME (sometimes called EXP or DEXPTIME) is the set of all decision problems that have exponential runtime, i.e., that are solvable by a deterministic Turing machine in O(2p(n)) time, where p(n) is a polynomial function of n. In terms of DTIME, We know and also, by the time hierarchy theorem and the space hierarchy theorem, that so at least one of the first three inclusions and at least one of the last three inclusions must be proper, but it is not known which ones are.
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Formal language
In mathematics, computer science, and linguistics, a formal language is a set of strings of symbols together with a set of rules that are specific to it.
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Game complexity
Combinatorial game theory has several ways of measuring game complexity.
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Hamiltonian path
In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once.
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Interactive proof system
In computational complexity theory, an interactive proof system is an abstract machine that models computation as the exchange of messages between two parties.
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Mihalis Yannakakis
Mihalis Yannakakis (Μιχάλης Γιαννακάκης; born 13 September 1953 in Athens, Greece) (accessed 12 November 2009) is Professor of Computer Science at Columbia University.
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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(kn) for some k. NE, unlike the similar class NEXPTIME, is not closed under polynomial-time many-one reductions.
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Non-deterministic Turing machine
In theoretical computer science, a Turing machine is a theoretical machine that is used in thought experiments to examine the abilities and limitations of computers.
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NP (complexity)
In computational complexity theory, NP (for nondeterministic polynomial time) is a complexity class used to describe certain types of decision problems.
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NP-completeness
In computational complexity theory, an NP-complete decision problem is one belonging to both the NP and the NP-hard complexity classes.
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NTIME
In computational complexity theory, the complexity class NTIME(f(n)) is the set of decision problems that can be solved by a non-deterministic Turing machine which runs in time O(f(n)).
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P (complexity)
In computational complexity theory, P, also known as PTIME or DTIME(nO(1)), is a fundamental complexity class.
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P versus NP problem
The P versus NP problem is a major unsolved problem in computer science.
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Padding argument
In computational complexity theory, the padding argument is a tool to conditionally prove that if some complexity classes are equal, then some other bigger classes are also equal.
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Polynomial-time reduction
In computational complexity theory, a polynomial-time reduction is a method of solving one problem by means of a hypothetical subroutine for solving a different problem (that is, a reduction), that uses polynomial time excluding the time within the subroutine.
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Probabilistically checkable proof
In computational complexity theory, a probabilistically checkable proof (PCP) is a type of proof that can be checked by a randomized algorithm using a bounded amount of randomness and reading a bounded number of bits of the proof.
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Sparse language
In computational complexity theory, a sparse language is a formal language (a set of strings) such that the complexity function, counting the number of strings of length n in the language, is bounded by a polynomial function of n. They are used primarily in the study of the relationship of the complexity class NP with other classes.
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Time complexity
In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.
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Time hierarchy theorem
In computational complexity theory, the time hierarchy theorems are important statements about time-bounded computation on Turing machines.
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References
[1] https://en.wikipedia.org/wiki/NEXPTIME
