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Adleman's Theorem
In computational complexity theory, P/poly is a complexity class that can be defined in both circuit complexity and non-uniform complexity. Since the two definitions are equivalent, this concept bridges the two areas. In the perspective of circuit complexity, P/poly is the class of problems that can be solved by small circuits. More precisely, it is the set of formal languages that have polynomial-size circuit families. In the perspective of non-uniform complexity, P/poly is defined in terms of Turing machines with advice, extra information supplied to the Turing machine along with its input, that may depend on the input length but not on the input itself. In this formulation, P/poly is the class of decision problems that can be solved by a polynomial-time Turing machine with advice strings of length polynomial in the input size. For example, the popular Miller–Rabin primality test can be formulated as a P/poly algorithm: the "advice" is a list of candidate values to test. It ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Computational Complexity Theory
In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and explores the relationships between these classifications. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used. The theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantifying their computational complexity, i.e., the amount of resources needed to solve them, such as time and storage. Other measures of complexity are also used, such as the amount of communication (used in communication complexity), the number of logic gate, gates in a circuit (used in circuit complexity) and the number of processors (used in parallel computing). O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Arthur–Merlin Protocol
In computational complexity theory, an Arthur–Merlin protocol, introduced by , is an interactive proof system in which the verifier's coin tosses are constrained to be public (i.e. known to the prover too). proved that all (formal) languages with interactive proofs of arbitrary length with private coins also have interactive proofs with public coins. Given two participants in the protocol called Arthur and Merlin respectively, the basic assumption is that Arthur is a standard computer (or verifier) equipped with a random number generating device, while Merlin is effectively an oracle with infinite computational power (also known as a prover). However, Merlin is not necessarily honest, so Arthur must analyze the information provided by Merlin in response to Arthur's queries and decide the problem itself. A problem is considered to be solvable by this protocol if whenever the answer is "yes", Merlin has some series of responses which will cause Arthur to accept at least of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Polynomial-time Turing Reduction
In computational complexity theory, a polynomial-time reduction is a method for solving one problem using another. One shows that if a hypothetical subroutine solving the second problem exists, then the first problem can be solved by transforming or reducing it to inputs for the second problem and calling the subroutine one or more times. If both the time required to transform the first problem to the second, and the number of times the subroutine is called is polynomial, then the first problem is polynomial-time reducible to the second. A polynomial-time reduction proves that the first problem is no more difficult than the second one, because whenever an efficient algorithm exists for the second problem, one exists for the first problem as well. By contraposition, if no efficient algorithm exists for the first problem, none exists for the second either. Polynomial-time reductions are frequently used in complexity theory for defining both complexity classes and complete problems ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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. The complexity class of all sparse languages is called SPARSE. Sparse languages are called ''sparse'' because there are a total of 2''n'' strings of length ''n'', and if a language only contains polynomially many of these, then the proportion of strings of length ''n'' that it contains rapidly goes to zero as ''n'' grows. All unary languages are sparse. An example of a nontrivial sparse language is the set of binary strings containing exactly ''k'' 1 bits for some fixed ''k''; for each ''n'', there are only \binom strings in the language, which is bounded by ''n''''k''. Relationships to other complexity classes * SPARSE contains TALLY, th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Rainbow Table
A rainbow table is a precomputed table for caching the outputs of a cryptographic hash function, usually for cracking password hashes. Passwords are typically stored not in plain text form, but as hash values. If such a database of hashed passwords falls into the hands of attackers, they can use a precomputed rainbow table to recover the plaintext passwords. A common defense against this attack is to compute the hashes using a key derivation function that adds a "salt" to each password before hashing it, with different passwords receiving different salts, which are stored in plain text along with the hash. Rainbow tables are a practical example of a space–time tradeoff: they use less computer processing time and more storage than a brute-force attack which calculates a hash on every attempt, but more processing time and less storage than a simple table that stores the hash of every possible password. Rainbow tables were invented by Philippe Oechslin as an application of an ea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Cryptography
Cryptography, or cryptology (from "hidden, secret"; and ''graphein'', "to write", or ''-logy, -logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of Adversary (cryptography), adversarial behavior. More generally, cryptography is about constructing and analyzing Communication protocol, protocols that prevent third parties or the public from reading private messages. Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, information security, electrical engineering, digital signal processing, physics, and others. Core concepts related to information security (confidentiality, data confidentiality, data integrity, authentication, and non-repudiation) are also central to cryptography. Practical applications of cryptography include electronic commerce, Smart card#EMV, chip-based payment cards, digital currencies, password, computer passwords, and military communications. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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. Example The proof that P (complexity), P = NP (complexity), NP implies EXP = NEXP uses "padding". \mathrm \subseteq \mathrm by definition, so it suffices to show \mathrm \subseteq \mathrm. Let ''L'' be a language in NEXP. Since ''L'' is in NEXP, there is a non-deterministic Turing machine ''M'' that decides ''L'' in time 2^ for some constant ''c''. Let : L'=\, where '1' is a symbol not occurring in ''L''. First we show that L' is in NP, then we will use the deterministic polynomial time machine given by P = NP to show that ''L'' is in EXP. L' can be Decision problem, decided in non-deterministic polynomial time as follows. Given input x', verify that it has the form x' = x1^ and reject if it does not. If it has the correct form, simulate ''M''(''x''). The simu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Journal Of Computer And System Sciences
The ''Journal of Computer and System Sciences'' (JCSS) is a peer-reviewed scientific journal in the field of computer science. ''JCSS'' is published by Elsevier, and it was started in 1967. Many influential scientific articles have been published in ''JCSS''; these include five papers that have won the Gödel Prize The Gödel Prize is an annual prize for outstanding papers in the area of theoretical computer science, given jointly by the European Association for Theoretical Computer Science (EATCS) and the Association for Computing Machinery Special Inter .... Its managing editor is Michael Segal. Notes References * * External links * Journal homepageScienceDirect accessDBLP information Computer science journals Elsevier academic journals {{compu-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
NEXPTIME
In computational complexity theory, the complexity class NEXPTIME (sometimes called NEXP) is the set of decision problems that can be solved by a non-deterministic Turing machine using time 2^. In terms of NTIME, :\mathsf = \bigcup_ \mathsf(2^) Alternatively, NEXPTIME can be defined using deterministic Turing machines as verifiers. A language ''L'' is in NEXPTIME if and only if there exist polynomials ''p'' and ''q'', and a deterministic Turing machine ''M'', such that * For all ''x'' and ''y'', the machine ''M'' runs in time 2^ on input * For all ''x'' in ''L'', there exists a string ''y'' of length 2^ such that * For all ''x'' not in ''L'' and all strings ''y'' of length 2^, We know : and also, by the time hierarchy theorem, that : If , then ( padding argument); more precisely, if and only if there exist sparse languages in NP that are not in P. Alternative characterizations In descriptive complexity, the sets of natural numbers that can be recognized in NEXPTIME ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
EXPTIME
In computational complexity theory, the complexity class EXPTIME (sometimes called EXP or DEXPTIME) is the set of all decision problems that are solvable by a deterministic Turing machine in exponential time, i.e., in O(2''p''(''n'')) time, where ''p''(''n'') is a polynomial function of ''n''. EXPTIME is one intuitive class in an exponential hierarchy of complexity classes with increasingly more complex oracles or quantifier alternations. For example, the class 2-EXPTIME is defined similarly to EXPTIME but with a doubly exponential time bound. This can be generalized to higher and higher time bounds. EXPTIME can also be reformulated as the space class APSPACE, the set of all problems that can be solved by an alternating Turing machine in polynomial space. EXPTIME relates to the other basic time and space complexity classes in the following way: P ⊆ NP ⊆ PSPACE ⊆ EXPTIME ⊆ NEXPTIME ⊆ EXPSPACE. Furthermore, by the time hierarchy theorem and the space hiera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Permanent Is Sharp-P-complete , Buddhist concept
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Permanent may refer to: Art and entertainment * ''Permanent'' (film), a 2017 American film * ''Permanent'' (Joy Division album) * "Permanent" (song), by David Cook *"Permanent", a song by Alex Lahey from ''The Answer Is Always Yes'', 2023 Other uses *Permanent (mathematics), a concept in linear algebra *Permanent (cycling event) *Permanent wave, a hairstyling process See also *Permanence (other) *''Permanently'', a 2000 album by Mark Wills *Endless (other) *Eternal (other) *Forever (other) *Impermanence Impermanence, also known as the philosophical problem of change, is a philosophical concept addressed in a variety of religions and philosophies. In Eastern philosophy it is notable for its role in the Buddhism, Buddhist three marks of existe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Sharp P
Sharp or SHARP may refer to: Acronyms * SHARP (helmet ratings) (Safety Helmet Assessment and Rating Programme), a British motorcycle helmet safety rating scheme * Self Help Addiction Recovery Program, a charitable organisation founded in 1991 by Barbara Bach and Pattie Boyd * Sexual Harassment/Assault Response & Prevention, a US Army program dealing with sexual harassment * Skinheads Against Racial Prejudice, an anti-racist Trojan skinhead organization formed to combat White power skinheads * Society for the History of Authorship, Reading and Publishing * Stationary High Altitude Relay Platform, a 1980s beamed-power aircraft * Super High Altitude Research Project, a 1990s project to develop a high-velocity gun * SIGINT High Altitude Replenishment Program (SHARP) Companies * I. P. Sharp Associates, a former Canadian computer services company * Sharp Airlines, an Australian regional airline * Sharp Corporation, a Japanese electronics manufacturer ** Sharp Solar, a manufactur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
