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Tree Stack Automaton
A tree stack automaton (plural: tree stack automata) is a formalism considered in automata theory. It is a finite-state automaton with the additional ability to manipulate a tree-shaped stack. It is an automaton with storageScott, Dana (1967). ''Some Definitional Suggestions for Automata Theory''. Journal of Computer and System Sciences, Vol. 1(2), pages 187–212doi:10.1016/s0022-0000(67)80014-x whose storage roughly resembles the configurations of a thread automaton. A restricted class of tree stack automata recognises exactly the languages generated by multiple context-free grammarsDenkinger, Tobias (2016). ''An automata characterisation for multiple context-free languages''. Proceedings of the 20th International Conference on Developments in Language Theory (DLT 2016). Lecture Notes in Computer Science, Vol. 9840, pages 138–150doi:10.1007/978-3-662-53132-7_12 (or linear context-free rewriting systems). Definition Tree stack For a finite and non-empty set , a ''tree stack o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formalism (philosophy Of Mathematics)
In the philosophy of mathematics, formalism is the view that holds that statements of mathematics and logic can be considered to be statements about the consequences of the manipulation of strings (alphanumeric sequences of symbols, usually as equations) using established manipulation rules. A central idea of formalism "is that mathematics is not a body of propositions representing an abstract sector of reality, but is much more akin to a game, bringing with it no more commitment to an ontology of objects or properties than ludo or chess." According to formalism, mathematical statements are not "about" numbers, sets, triangles, or any other mathematical objects in the way that physical statements are about material objects. Instead, they are purely syntactic expressions—formal strings of symbols manipulated according to explicit rules without inherent meaning. These symbolic expressions only acquire interpretation (or semantics) when we choose to assign it, similar to how che ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unary Operation
In mathematics, a unary operation is an operation with only one operand, i.e. a single input. This is in contrast to ''binary operations'', which use two operands. An example is any function , where is a set; the function is a unary operation on . Common notations are prefix notation (e.g. ¬, −), postfix notation (e.g. factorial ), functional notation (e.g. or ), and superscripts (e.g. transpose ). Other notations exist as well, for example, in the case of the square root, a horizontal bar extending the square root sign over the argument can indicate the extent of the argument. Examples Absolute value Obtaining the absolute value of a number is a unary operation. This function is defined as , n, = \begin n, & \mbox n\geq0 \\ -n, & \mbox n<0 \end where is the absolute value of . Negation |
Pushdown Automaton
In the theory of computation, a branch of theoretical computer science, a pushdown automaton (PDA) is a type of automaton that employs a stack. Pushdown automata are used in theories about what can be computed by machines. They are more capable than finite-state machines but less capable than Turing machines (see below). Deterministic pushdown automata can recognize all deterministic context-free languages while nondeterministic ones can recognize all context-free languages, with the former often used in parser design. The term "pushdown" refers to the fact that the stack can be regarded as being "pushed down" like a tray dispenser at a cafeteria, since the operations never work on elements other than the top element. A stack automaton, by contrast, does allow access to and operations on deeper elements. Stack automata can recognize a strictly larger set of languages than pushdown automata. A nested stack automaton allows full access, and also allows stacked values to be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turing Machine
A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any computer algorithm. The machine operates on an infinite memory tape divided into discrete mathematics, discrete cells, each of which can hold a single symbol drawn from a finite set of symbols called the Alphabet (formal languages), alphabet of the machine. It has a "head" that, at any point in the machine's operation, is positioned over one of these cells, and a "state" selected from a finite set of states. At each step of its operation, the head reads the symbol in its cell. Then, based on the symbol and the machine's own present state, the machine writes a symbol into the same cell, and moves the head one step to the left or the right, or halts the computation. The choice of which replacement symbol to write, which direction to move the head, and whet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Relation
In mathematics, a binary relation associates some elements of one Set (mathematics), set called the ''domain'' with some elements of another set called the ''codomain''. Precisely, a binary relation over sets X and Y is a set of ordered pairs (x, y), where x is an element of X and y is an element of Y. It encodes the common concept of relation: an element x is ''related'' to an element y, if and only if the pair (x, y) belongs to the set of ordered pairs that defines the binary relation. An example of a binary relation is the "divides" relation over the set of prime numbers \mathbb and the set of integers \mathbb, in which each prime p is related to each integer z that is a Divisibility, multiple of p, but not to an integer that is not a Multiple (mathematics), multiple of p. In this relation, for instance, the prime number 2 is related to numbers such as -4, 0, 6, 10, but not to 1 or 9, just as the prime number 3 is related to 0, 6, and 9, but not to 4 or 13. Binary relations ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Set On A Tree Stack
Set, The Set, SET or SETS may refer to: Science, technology, and mathematics Mathematics *Set (mathematics), a collection of elements *Category of sets, the category whose objects and morphisms are sets and total functions, respectively Electronics and computing *Set (abstract data type), a data type in computer science that is a collection of unique values ** Set (C++), a set implementation in the C++ Standard Library * Set (command), a command for setting values of environment variables in Unix and Microsoft operating-systems * Secure Electronic Transaction, a standard protocol for securing credit card transactions over insecure networks * Single-electron transistor, a device to amplify currents in nanoelectronics * Single-ended triode, a type of electronic amplifier * Set!, a programming syntax in the scheme programming language Biology and psychology * Set (psychology), a set of expectations which shapes perception or thought *Set or sett, a badger's den *Set, a small tuber ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Push On A Tree Stack
Push may refer to: * A type of force applied to an object Music * Mike Dierickx (born 1973), a Belgian producer also known as Push Albums * ''Push'' (Bros album), 1988 * ''Push'' (Gruntruck album), 1992 * ''Push'' (Jacky Terrasson album), 2010 * ''Push'' (Sextile album), 2023 Songs * "Push" (Enrique Iglesias song), 2008 * "Push" (Avril Lavigne song), 2011 * "Push" (Lenny Kravitz song), 2011 * "Push" (Matchbox Twenty song), 1997 * "Push" (Moist song), 1994 * "Push" (Pharoahe Monch song), 2006 * "Push", by Tisha Campbell and Vanilla Ice on Campbell's 1993 album '' Tisha'' * "Push", by The Cure on the 1985 album ''The Head on the Door'' * "Push", by Dio on the 2002 album '' Killing the Dragon'' * "Push", by Nick Jonas on the 2014 album ''Nick Jonas'' * "Push", by Madonna on the 2005 album ''Confessions on a Dance Floor'' * "Push", by Marianas Trench on the 2006 album '' Fix Me'' * "Push", by Sarah McLachlan on the 2003 album ''Afterglow'' * "Push", by Dannii Minogue on the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Id On A Tree Stack
ID or its variants may refer to: * Identity document, a document used to verify a person's identity * Identifier, a symbol which uniquely identifies an object or record People * I. D. Ffraid (1814–1875), Welsh poet and Calvinistic Methodist minister * I. D. McMaster (1923–2004), American assistant district attorney * I. D. Serebryakov (1917–1998), Russian lexicographer and translator Places * İd or Narman, a town in Turkey * Idaho, US (postal abbreviation ID) * Indonesia, ISO 3166-1 alpha-2 country code "ID" ** Indonesian language, ISO 639-1 language code "ID" Arts, entertainment, and media Music * The Id (band), an English new wave/synthpop band * New:ID, an upcoming Filipino boy band Albums * ''I.D.'' (album), a 1989 album by The Wailers Band * ''ID'' (Michael Patrick Kelly album), a 2017 studio album by Michael Patrick Kelly * ''Id'' (Siddharta album), 1999 * '' d' (Veil of Maya album), 2010 * ''ID'', an album by Anna Maria Jopek * ''The Id'' (album), a 2001 s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Predicate (mathematical Logic)
In logic, a predicate is a symbol that represents a property or a relation. For instance, in the first-order formula P(a), the symbol P is a predicate that applies to the individual constant a. Similarly, in the formula R(a,b), the symbol R is a predicate that applies to the individual constants a and b. According to Gottlob Frege, the meaning of a predicate is exactly a function from the domain of objects to the truth values "true" and "false". In the semantics of logic, predicates are interpreted as relations. For instance, in a standard semantics for first-order logic, the formula R(a,b) would be true on an interpretation if the entities denoted by a and b stand in the relation denoted by R. Since predicates are non-logical symbols, they can denote different relations depending on the interpretation given to them. While first-order logic only includes predicates that apply to individual objects, other logics may allow predicates that apply to collections of objects defin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Domain Of A Function
In mathematics, the domain of a function is the Set (mathematics), set of inputs accepted by the Function (mathematics), function. It is sometimes denoted by \operatorname(f) or \operatornamef, where is the function. In layman's terms, the domain of a function can generally be thought of as "what x can be". More precisely, given a function f\colon X\to Y, the domain of is . In modern mathematical language, the domain is part of the definition of a function rather than a property of it. In the special case that and are both sets of real numbers, the function can be graphed in the Cartesian coordinate system. In this case, the domain is represented on the -axis of the graph, as the projection of the graph of the function onto the -axis. For a function f\colon X\to Y, the set is called the ''codomain'': the set to which all outputs must belong. The set of specific outputs the function assigns to elements of is called its ''Range of a function, range'' or ''Image (mathematic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
