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Tag System
In the theory of computation, a tag system is a deterministic model of computation published by Emil Leon Post in 1943 as a simple form of a Post canonical system. A tag system may also be viewed as an abstract machine, called a Post tag machine (not to be confused with Post–Turing machines)—briefly, a finite-state machine whose only tape is a FIFO queue of unbounded length, such that in each transition the machine reads the symbol at the head of the queue, deletes a constant number of symbols from the head, and appends to the tail a symbol-string that depends solely on the first symbol read in this transition. Because all of the indicated operations are performed in a single transition, a tag machine strictly has only one state. Definitions A ''tag system'' is a triplet (''m'', ''A'', ''P''), where * ''m'' is a positive integer, called the ''deletion number''. * ''A'' is a finite alphabet of symbols, one of which can be a special ''halting symbol''. All finite (possibl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theory Of Computation
In theoretical computer science and mathematics, the theory of computation is the branch that deals with what problems can be solved on a model of computation, using an algorithm, how efficiently they can be solved or to what degree (e.g., approximate solutions versus precise ones). The field is divided into three major branches: automata theory and formal languages, computability theory, and computational complexity theory, which are linked by the question: ''"What are the fundamental capabilities and limitations of computers?".'' In order to perform a rigorous study of computation, computer scientists work with a mathematical abstraction of computers called a model of computation. There are several models in use, but the most commonly examined is the Turing machine. Computer scientists study the Turing machine because it is simple to formulate, can be analyzed and used to prove results, and because it represents what many consider the most powerful possible "reasonable" m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Undecidable Problem
In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is proved to be impossible to construct an algorithm that always leads to a correct yes-or-no answer. The halting problem is an example: it can be proven that there is no algorithm that correctly determines whether an arbitrary program eventually halts when run. Background A decision problem is a question which, for every input in some infinite set of inputs, requires a "yes" or "no" answer. Those inputs can be numbers (for example, the decision problem "is the input a prime number?") or values of some other kind, such as strings of a formal language. The formal representation of a decision problem is a subset of the natural numbers. For decision problems on natural numbers, the set consists of those numbers that the decision problem answers "yes" to. For example, the decision problem "is the input even?" is formalized as the set of even numbers. A decision pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theoretical Computer Science
Theoretical computer science is a subfield of computer science and mathematics that focuses on the Abstraction, abstract and mathematical foundations of computation. It is difficult to circumscribe the theoretical areas precisely. The Association for Computing Machinery, ACM's Special Interest Group on Algorithms and Computation Theory (SIGACT) provides the following description: History While logical inference and mathematical proof had existed previously, in 1931 Kurt Gödel proved with his incompleteness theorem that there are fundamental limitations on what statements could be proved or disproved. Information theory was added to the field with A Mathematical Theory of Communication, a 1948 mathematical theory of communication by Claude Shannon. In the same decade, Donald Hebb introduced a mathematical model of Hebbian learning, learning in the brain. With mounting biological data supporting this hypothesis with some modification, the fields of neural networks and para ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Journal Of Mathematics
The ''American Journal of Mathematics'' is a bimonthly mathematics journal published by the Johns Hopkins University Press. History The ''American Journal of Mathematics'' is the oldest continuously published mathematical journal in the United States, established in 1878 at the Johns Hopkins University by James Joseph Sylvester, an English-born mathematician who also served as the journal's editor-in-chief from its inception through early 1884. Initially W. E. Story was associate editor in charge; he was replaced by Thomas Craig (mathematician), Thomas Craig in 1880. For volume 7 Simon Newcomb became chief editor with Craig managing until 1894. Then with volume 16 it was "Edited by Thomas Craig with the Co-operation of Simon Newcomb" until 1898. Other notable mathematicians who have served as editors or editorial associates of the journal include Frank Morley, Oscar Zariski, Lars Ahlfors, Hermann Weyl, Wei-Liang Chow, S. S. Chern, André Weil, Harish-Chandra, Jean Dieudonné, Hen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prentice–Hall
Prentice Hall was a major American educational publisher. It published print and digital content for the 6–12 and higher-education market. It was an independent company throughout the bulk of the twentieth century. In its last few years it was owned by, then absorbed into, Savvas Learning Company. In the Web era, it distributed its technical titles through the Safari Books Online e-reference service for some years. History On October 13, 1913, law professor Charles Gerstenberg and his student Richard Ettinger founded Prentice Hall. Gerstenberg and Ettinger took their mothers' maiden names, Prentice and Hall, to name their new company. At the time the name was usually styled as Prentice-Hall (as seen for example on many title pages), per an orthographic norm for coordinate elements within such compounds (compare also ''McGraw-Hill'' with later styling as ''McGraw Hill''). Prentice-Hall became known as a publisher of trade books by authors such as Norman Vincent Peale; eleme ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annals Of Mathematics
The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as the founding editor-in-chief. It was "intended to afford a medium for the presentation and analysis of any and all questions of interest or importance in pure and applied Mathematics, embracing especially all new and interesting discoveries in theoretical and practical astronomy, mechanical philosophy, and engineering". It was published in Des Moines, Iowa, and was the earliest American mathematics journal to be published continuously for more than a year or two. This incarnation of the journal ceased publication after its tenth year, in 1883, giving as an explanation Hendricks' declining health, but Hendricks made arrangements to have it taken over by new management, and it was continued from March 1884 as the ''Annals of Mathematics''. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conway's Game Of Life
The Game of Life, also known as Conway's Game of Life or simply Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is a zero-player game, meaning that its evolution is determined by its initial state, requiring no further input. One interacts with the Game of Life by creating an initial configuration and observing how it evolves. It is Turing complete and can simulate a von Neumann universal constructor, universal constructor or any other Turing machine. Rules The universe of the Game of Life is Square tiling, an infinite, two-dimensional orthogonal grid of square ''cells'', each of which is in one of two possible states, ''live'' or ''dead'' (or ''populated'' and ''unpopulated'', respectively). Every cell interacts with its eight ''Moore neighborhood, neighbours'', which are the cells that are horizontally, vertically, or diagonally adjacent. At each step in time, the following transitions occur: # Any live cell with fewer than ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Queue Automaton
A queue machine, queue automaton, or pullup automaton (PUA) is a finite-state machine with the ability to store and retrieve data from an infinite-memory queue. Its design is similar to a pushdown automaton but differs by replacing the stack with this queue. A queue machine is a model of computation equivalent to a Turing machine, and therefore it can process the same class of formal languages. Theory A queue machine can be defined as a six-tuple :M = (Q, \Sigma, \Gamma, \$, s, \delta) where * \,Q is a finite set of ''states''; * \,\Sigma \subset \Gamma is the finite set of the ''input alphabet''; * \,\Gamma is the finite ''queue alphabet''; * \,\$ \in \Gamma \setminus \Sigma is the ''initial queue symbol''; * \,s \in Q is the ''start state''; * \,\delta : Q \times \Gamma \rightarrow Q \times \Gamma^* is the ''transition function''. A machine ''configuration'' is an ordered pair of its state and queue contents \,(q,\gamma)\in Q\times\Gamma^*, where \,\Gamma^* denotes the Klee ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turing-complete
In computability theory, a system of data-manipulation rules (such as a model of computation, a computer's instruction set, a programming language, or a cellular automaton) is said to be Turing-complete or computationally universal if it can be used to simulate any Turing machine (devised by English mathematician and computer scientist Alan Turing). This means that this system is able to recognize or decode other data-manipulation rule sets. Turing completeness is used as a way to express the power of such a data-manipulation rule set. Virtually all programming languages today are Turing-complete. A related concept is that of Turing equivalence two computers P and Q are called equivalent if P can simulate Q and Q can simulate P. The Church–Turing thesis conjectures that any function whose values can be computed by an algorithm can be computed by a Turing machine, and therefore that if any real-world computer can simulate a Turing machine, it is Turing equivalent to a Turing ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rule 110
The Rule 110 cellular automaton (often called simply Rule 110) is an elementary cellular automaton with interesting behavior on the boundary between stability and chaos. In this respect, it is similar to Conway's Game of Life. Like Life, Rule 110 with a particular repeating background pattern is known to be Turing complete. This implies that, in principle, any calculation or computer program can be simulated using this automaton. Definition In an elementary cellular automaton, a one-dimensional pattern of 0s and 1s evolves according to a simple set of rules. Whether a point in the pattern will be 0 or 1 in the new generation depends on its current value, as well as on those of its two neighbors. The Rule 110 automaton has the following set of rules: The name "Rule 110" derives from the fact that this rule can be summarized in the binary sequence 01101110; interpreted as a binary number, this corresponds to the decimal value 110. This is the Wolfram code naming scheme. Hi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matthew Cook
Matthew Cook (born February 7, 1970) is a mathematician and computer scientist who is best known for having proved Stephen Wolfram's conjecture that the Rule 110 cellular automaton is Turing-complete. Biography Cook was born in Morgantown, West Virginia and grew up in Evanston, Illinois. He completed his undergraduate studies at the University of Illinois and the Budapest Semesters in Mathematics program. In 1987, Cook qualified as a member of the six-person US team to the International Mathematical Olympiad and won a bronze medal. In 1990, Cook went to work for Wolfram Research, makers of the computer algebra system Mathematica. He did his doctoral work in Computation and Neural Systems at Caltech from 1999 to 2005. He is now at the Institute of Neuroinformatics at Zurich in Switzerland. Work with Stephen Wolfram In the 1990s Cook worked as a research assistant to Stephen Wolfram, assisting with work on Wolfram's book, ''A New Kind of Science''. Among other things, he developed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tag (game)
Tag (also called chase, tig, it, tiggy, tips, tick, on-on and tip) is a playground game involving one or more players chasing other players in an attempt to "tag" and mark them out of play, typically by touching with a hand. There are many variations; most forms have no teams, scores, or equipment. Usually when a person is tagged, the tagger says, "It!", "Tag, you're 'It'!" or "Tag". The last one tagged during tag is "It" for the next round. The game is known by other names in various parts of the world, including "running and catching" in India and "catch and cook" in the Middle East. Origin of name The game has many different names in different parts of the UK: 'tig' in Yorkshire, Scotland, and in the North West of England; and 'it' in the South of England. In the United States the game is usually called 'tag', and in Australia it is sometimes called 'tips'. In 2018, the internet meme "How old were you when you found out ____" began circulating, which stated that the orig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
