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Pumping Lemma
In the theory of 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 sym ...s, the pumping lemma may refer to: * Pumping lemma for regular languages, the fact that all sufficiently long strings in such a language have a substring that can be repeated arbitrarily many times, usually used to prove that certain languages are not regular * Pumping lemma for context-free languages, the fact that all sufficiently long strings in such a language have a pair of substrings that can be repeated arbitrarily many times, usually used to prove that certain languages are not context-free * Pumping lemma for indexed languages * Pumping lemma for regular tree languages See also * Ogden's lemma, a stronger version of the pumping lemma for context-free languages {{sia ... [...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 compl ... [...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) {{single source, date=February 2019 Pumping is a skateboarding technique used to accelerate without the rider's feet leaving the board. Pumping can be done by turning or on a transition, like a ramp or quarter pipe.https://skateboarding.transwor ..., accelerating without pushing off of the ground * "Pumping" (My Heart) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pumping Lemma For Context-free 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) {{single source, date=February 2019 Pumping is a skateboarding technique used to accelerate without the rider's feet leaving the board. Pumping can be done by turning or on a transition, like a ramp or quarter pipe.https://skateboarding.transwor ..., accelerating without pushing off of the ground * "Pumping" (My Heart) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indexed Language
Indexed languages are a class of formal languages discovered by Alfred Aho; they are described by indexed grammars and can be recognized by nested stack automata. Indexed languages are a proper subset of context-sensitive languages. They qualify as an abstract family of languages (furthermore a full AFL) and hence satisfy many closure properties. However, they are not closed under intersection or complement. The class of indexed languages has generalization of context-free languages, since indexed grammars can describe many of the nonlocal constraints occurring in natural languages. Gerald Gazdar (1988) and Vijay-Shanker (1987) introduced a mildly context-sensitive language class now known as linear indexed grammars (LIG). Linear indexed grammars have additional restrictions relative to IG. LIGs are weakly equivalent (generate the same language class) as tree adjoining grammars. Examples The following languages are indexed, but are not context-free: : \ : \ These two l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pumping Lemma For Regular Tree Languages
A tree automaton is a type of state machine. Tree automata deal with tree structures, rather than the strings of more conventional state machines. The following article deals with branching tree automata, which correspond to regular languages of trees. As with classical automata, finite tree automata (FTA) can be either a deterministic automaton or not. According to how the automaton processes the input tree, finite tree automata can be of two types: (a) bottom up, (b) top down. This is an important issue, as although non-deterministic (ND) top-down and ND bottom-up tree automata are equivalent in expressive power, deterministic top-down automata are strictly less powerful than their deterministic bottom-up counterparts, because tree properties specified by deterministic top-down tree automata can only depend on path properties. (Deterministic bottom-up tree automata are as powerful as ND tree automata.) Definitions A bottom-up finite tree automaton over ''F'' is defined as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
