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ACC0
ACC0, sometimes called ACC, is a class of computational models and problems defined in circuit complexity, a field of theoretical computer science. The class is defined by augmenting the class AC0, AC0 of constant-depth "alternating circuits" with the ability to count; the acronym ACC stands for "AC with counters"., p. 126 Specifically, a problem belongs to ACC0 if it can be solved by polynomial-size, constant-depth circuits of unbounded fan-in gates, including gates that count modulo a fixed integer. ACC0 corresponds to computation in any solvable monoid. The class is very well studied in theoretical computer science because of the algebraic connections and because it is one of the largest concrete computational models for which computational impossibility results, so-called circuit lower bounds, can be proved. Definitions Informally, ACC0 models the class of computations realised by Boolean circuits of constant depth and polynomial size, where the circuit gates includes "modular ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circuit Complexity
In theoretical computer science, circuit complexity is a branch of computational complexity theory in which Boolean functions are classified according to the size or depth of the Boolean circuits that compute them. A related notion is the circuit complexity of a recursive language that is decided by a uniform family of circuits C_,C_,\ldots (see below). Proving lower bounds on size of Boolean circuits computing explicit Boolean functions is a popular approach to separating complexity classes. For example, a prominent circuit class P/poly consists of Boolean functions computable by circuits of polynomial size. Proving that \mathsf\not\subseteq \mathsf would separate P and NP (see below). Complexity classes defined in terms of Boolean circuits include AC0, AC, TC0, NC1, NC, and P/poly. Size and depth A Boolean circuit with n input bits is a directed acyclic graph in which every node (usually called ''gates'' in this context) is either an input node of in-degree 0 labelle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circuit Complexity
In theoretical computer science, circuit complexity is a branch of computational complexity theory in which Boolean functions are classified according to the size or depth of the Boolean circuits that compute them. A related notion is the circuit complexity of a recursive language that is decided by a uniform family of circuits C_,C_,\ldots (see below). Proving lower bounds on size of Boolean circuits computing explicit Boolean functions is a popular approach to separating complexity classes. For example, a prominent circuit class P/poly consists of Boolean functions computable by circuits of polynomial size. Proving that \mathsf\not\subseteq \mathsf would separate P and NP (see below). Complexity classes defined in terms of Boolean circuits include AC0, AC, TC0, NC1, NC, and P/poly. Size and depth A Boolean circuit with n input bits is a directed acyclic graph in which every node (usually called ''gates'' in this context) is either an input node of in-degree 0 labelle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computing The Permanent
In linear algebra, the computation of the permanent of a matrix is a problem that is thought to be more difficult than the computation of the determinant of a matrix despite the apparent similarity of the definitions. The permanent is defined similarly to the determinant, as a sum of products of sets of matrix entries that lie in distinct rows and columns. However, where the determinant weights each of these products with a ±1 sign based on the parity of the set, the permanent weights them all with a +1 sign. While the determinant can be computed in polynomial time by Gaussian elimination, it is generally believed that the permanent cannot be computed in polynomial time. In computational complexity theory, a theorem of Valiant states that computing permanents is #P-hard, and even #P-complete for matrices in which all entries are 0 or 1 . This puts the computation of the permanent in a class of problems believed to be even more difficult to compute than NP. It is known tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theoretical Computer Science (journal)
''Theoretical Computer Science'' (TCS) is a computer science journal published by Elsevier, started in 1975 and covering theoretical computer science. The journal publishes 52 issues a year. It is abstracted and indexed by Scopus and the Science Citation Index. According to the Journal Citation Reports, its 2020 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as i ... is 0.827. References Computer science journals Elsevier academic journals Publications established in 1975 {{comp-sci-theory-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symposium On Theory Of Computing
The Annual ACM Symposium on Theory of Computing (STOC) is an academic conference in the field of theoretical computer science. STOC has been organized annually since 1969, typically in May or June; the conference is sponsored by the Association for Computing Machinery special interest group SIGACT. Acceptance rate of STOC, averaged from 1970 to 2012, is 31%, with the rate of 29% in 2012. As writes, STOC and its annual IEEE counterpart FOCS (the Symposium on Foundations of Computer Science) are considered the two top conferences in theoretical computer science, considered broadly: they “are forums for some of the best work throughout theory of computing that promote breadth among theory of computing researchers and help to keep the community together.” includes regular attendance at STOC and FOCS as one of several defining characteristics of theoretical computer scientists. Awards The Gödel Prize for outstanding papers in theoretical computer science is presented alternately a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer-Verlag
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business internationally, o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of The ACM
The ''Journal of the ACM'' is a peer-reviewed scientific journal covering computer science in general, especially theoretical aspects. It is an official journal of the Association for Computing Machinery. Its current editor-in-chief is Venkatesan Guruswami. The journal was established in 1954 and "computer scientists universally hold the ''Journal of the ACM'' in high esteem". See also * ''Communications of the ACM ''Communications of the ACM'' is the monthly journal of the Association for Computing Machinery (ACM). It was established in 1958, with Saul Rosen as its first managing editor. It is sent to all ACM members. Articles are intended for readers with ...'' References External links * Publications established in 1954 Computer science journals Association for Computing Machinery academic journals Bimonthly journals English-language journals {{compu-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. an 2014 Gödel Prize Its managing editor is |
SIAM Journal On Computing
The ''SIAM Journal on Computing'' is a scientific journal focusing on the mathematical and formal aspects of computer science. It is published by the Society for Industrial and Applied Mathematics (SIAM). Although its official ISO abbreviation is ''SIAM J. Comput.'', its publisher and contributors frequently use the shorter abbreviation ''SICOMP''. SICOMP typically hosts the special issues of the IEEE Annual Symposium on Foundations of Computer Science (FOCS) and the Annual ACM Symposium on Theory of Computing (STOC), where about 15% of papers published in FOCS and STOC each year are invited to these special issues. For example, Volume 48 contains 11 out of 85 papers published in FOCS 2016. References * External linksSIAM Journal on Computing on |
PP (complexity)
In complexity theory, PP is the class of decision problems solvable by a probabilistic Turing machine in polynomial time, with an error probability of less than 1/2 for all instances. The abbreviation PP refers to probabilistic polynomial time. The complexity class was defined by Gill in 1977. If a decision problem is in PP, then there is an algorithm for it that is allowed to flip coins and make random decisions. It is guaranteed to run in polynomial time. If the answer is YES, the algorithm will answer YES with probability more than 1/2. If the answer is NO, the algorithm will answer YES with probability less than 1/2. In more practical terms, it is the class of problems that can be solved to any fixed degree of accuracy by running a randomized, polynomial-time algorithm a sufficient (but bounded) number of times. Turing machines that are polynomially-bound and probabilistic are characterized as PPT, which stands for probabilistic polynomial-time machines. This characterization ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
DLOGTIME
In computational complexity theory, DLOGTIME is the complexity class of all computational problems solvable in a logarithmic amount of computation time on a deterministic Turing machine. It must be defined on a random-access Turing machine, since otherwise the input tape is longer than the range of cells that can be accessed by the machine. It is a very weak model of time complexity: no random-access Turing machine with a smaller deterministic time bound can access the whole input.. See in particulap. 140 Examples DLOGTIME includes problems relating to verifying the length of the input, for example the problem "''Is the input of even length?''", which can be solved in logarithmic time using binary search. Applications DLOGTIME- uniformity is important in circuit complexity In theoretical computer science, circuit complexity is a branch of computational complexity theory in which Boolean functions are classified according to the size or depth of the Boolean circuits that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Derandomization
A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic or procedure. The algorithm typically uses uniformly random bits as an auxiliary input to guide its behavior, in the hope of achieving good performance in the "average case" over all possible choices of random determined by the random bits; thus either the running time, or the output (or both) are random variables. One has to distinguish between algorithms that use the random input so that they always terminate with the correct answer, but where the expected running time is finite (Las Vegas algorithms, for example Quicksort), and algorithms which have a chance of producing an incorrect result (Monte Carlo algorithms, for example the Monte Carlo algorithm for the MFAS problem) or fail to produce a result either by signaling a failure or failing to terminate. In some cases, probabilistic algorithms are the only practical means of solving a problem. In common practice, randomized algor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
