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Counter Automaton
In computer science, more particular in the theory of formal languages, a counter automaton, or counter machine, is a pushdown automaton with only two symbols, A and the initial symbol in \Gamma, the finite set of stack symbols. Equivalently, a counter automaton is a nondeterministic finite automaton with an additional memory cell that can hold one nonnegative integer number (of unlimited size), which can be incremented, decremented, and tested for being zero. Properties The class of counter automata can recognize a proper superset of the regular and a subset of the deterministic context free languages. For example, the language \ is a non-regularby the pumping lemma for regular languages language accepted by a counter automaton: It can use the symbol A to count the number of as in a given input string x (writing an A for each a in x), after that, it can delete an A for each b in x. A two-counter automaton, that is, a two-stack Turing machine with a two-symbol alphabet, can si ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical disciplines (including the design and implementation of Computer architecture, hardware and Computer programming, software). Computer science is generally considered an area of research, academic research and distinct from computer programming. Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and for preventing Vulnerability (computing), security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Progr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Language
In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules. The alphabet of a formal language consists of symbols, letters, or tokens that concatenate into strings of the language. Each string concatenated from symbols of this alphabet is called a word, and the words that belong to a particular formal language are sometimes called ''well-formed words'' or ''well-formed formulas''. A formal language is often defined by means of a formal grammar such as a regular grammar or context-free grammar, which consists of its formation rules. In computer science, formal languages are used among others as the basis for defining the grammar of programming languages and formalized versions of subsets of natural languages in which the words of the language represent concepts that are associated with particular meanings or semantics. In computational complexity ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Nondeterministic Finite Automaton
In automata theory, a finite-state machine is called a deterministic finite automaton (DFA), if * each of its transitions is ''uniquely'' determined by its source state and input symbol, and * reading an input symbol is required for each state transition. A nondeterministic finite automaton (NFA), or nondeterministic finite-state machine, does not need to obey these restrictions. In particular, every DFA is also an NFA. Sometimes the term NFA is used in a narrower sense, referring to an NFA that is ''not'' a DFA, but not in this article. Using the subset construction algorithm, each NFA can be translated to an equivalent DFA; i.e., a DFA recognizing the same formal language. Like DFAs, NFAs only recognize regular languages. NFAs were introduced in 1959 by Michael O. Rabin and Dana Scott, who also showed their equivalence to DFAs. NFAs are used in the implementation of regular expressions: Thompson's construction is an algorithm for compiling a regular expression to an NFA that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regular Language
In theoretical computer science and formal language theory, a regular language (also called a rational language) is a formal language that can be defined by a regular expression, in the strict sense in theoretical computer science (as opposed to many modern regular expressions engines, which are augmented with features that allow recognition of non-regular languages). Alternatively, a regular language can be defined as a language recognized by a finite automaton. The equivalence of regular expressions and finite automata is known as Kleene's theorem (after American mathematician Stephen Cole Kleene). In the Chomsky hierarchy, regular languages are the languages generated by Type-3 grammars. Formal definition The collection of regular languages over an alphabet Σ is defined recursively as follows: * The empty language Ø is a regular language. * For each ''a'' ∈ Σ (''a'' belongs to Σ), the singleton language is a regular language. * If ''A'' is a regular language, ''A''* ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Automaton
A finite-state machine (FSM) or finite-state automaton (FSA, plural: ''automata''), finite automaton, or simply a state machine, is a mathematical model of computation. It is an abstract machine that can be in exactly one of a finite number of '' states'' at any given time. The FSM can change from one state to another in response to some inputs; the change from one state to another is called a ''transition''. An FSM is defined by a list of its states, its initial state, and the inputs that trigger each transition. Finite-state machines are of two types— deterministic finite-state machines and non-deterministic finite-state machines. A deterministic finite-state machine can be constructed equivalent to any non-deterministic one. The behavior of state machines can be observed in many devices in modern society that perform a predetermined sequence of actions depending on a sequence of events with which they are presented. Simple examples are vending machines, which dispense p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regular Language
In theoretical computer science and formal language theory, a regular language (also called a rational language) is a formal language that can be defined by a regular expression, in the strict sense in theoretical computer science (as opposed to many modern regular expressions engines, which are augmented with features that allow recognition of non-regular languages). Alternatively, a regular language can be defined as a language recognized by a finite automaton. The equivalence of regular expressions and finite automata is known as Kleene's theorem (after American mathematician Stephen Cole Kleene). In the Chomsky hierarchy, regular languages are the languages generated by Type-3 grammars. Formal definition The collection of regular languages over an alphabet Σ is defined recursively as follows: * The empty language Ø is a regular language. * For each ''a'' ∈ Σ (''a'' belongs to Σ), the singleton language is a regular language. * If ''A'' is a regular language, ''A''* ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deterministic Context Free Language
In formal language theory, deterministic context-free languages (DCFL) are a proper subset of context-free languages. They are the context-free languages that can be accepted by a deterministic pushdown automaton. DCFLs are always unambiguous, meaning that they admit an unambiguous grammar. There are non-deterministic unambiguous CFLs, so DCFLs form a proper subset of unambiguous CFLs. DCFLs are of great practical interest, as they can be parsed in linear time, and various restricted forms of DCFGs admit simple practical parsers. They are thus widely used throughout computer science. Description The notion of the DCFL is closely related to the deterministic pushdown automaton (DPDA). It is where the language power of pushdown automata is reduced to if we make them deterministic; the pushdown automata become unable to choose between different state-transition alternatives and as a consequence cannot recognize all context-free languages. Unambiguous grammars do not always genera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pumping Lemma For Regular Languages
Pumping may refer to: * The operation of a pump, for moving a liquid from one location to another **The use of a breast pump for extraction of milk * Pumping (audio), a creative misuse of dynamic range compression * Pumping (computer systems), the number of times data is transmitted per clock cycle * Pumping (oil well), injecting chemicals into a wellbore * Pumping (noise reduction), an unwanted artifact of some noise reduction systems * Pumping lemma, in the theory of formal languages * Gastric lavage, cleaning the contents of the stomach * Optical pumping, in which light is used to raise electrons from a lower energy level to a higher one * Pump (skateboarding), accelerating without pushing off of the ground * Pumping (My Heart), "Pumping" (My Heart), a 1976 song by Patti Smith Group {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multitape Turing Machine
A multi-tape Turing machine is a variant of the Turing machine that utilizes several tapes. Each tape has its own head for reading and writing. Initially, the input appears on tape 1, and the others start out blank. This model intuitively seems much more powerful than the single-tape model, but any multi-tape machine—no matter how many tapes—can be simulated by a single-tape machine using only quadratically more computation time. Thus, multi-tape machines cannot calculate any more functions than single-tape machines, and none of the robust complexity classes (such as polynomial time) are affected by a change between single-tape and multi-tape machines. Formal definition k -tape Turing machine can be formally defined as a 7-tuple M = \langle Q, \Gamma, b, \Sigma, \delta, q_0, F \rangle, following the notation of a Turing machine: * \Gamma is a finite, non-empty set of ''tape alphabet symbols''; * b \in \Gamma is the ''blank symbol'' (the only symbol allowed to occur on the ... [...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 cells, each of which can hold a single symbol drawn from a finite set of symbols called the 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 and which direction to move is based on a finite table that specifies what to do for each comb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
