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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 {a } is a regular language. If A is a regular language, A* (Kleene star) is a regular language. Due to this, the empty string language {ε} is also ...
The left-regular grammars describe the reverses of all such languages, that is, exactly the regular languages as well. Every strict right-regular grammar is extended right-regular, while every extended right-regular grammar can be made strict by inserting new non-terminals, such that the result generates the same language; hence, extended right ...
In the theory of formal languages, the pumping lemma for regular languages is a lemma that describes an essential property of all regular languages. Informally, it says that all sufficiently long strings in a regular language may be pumped —that is, have a middle section of the string repeated an arbitrary number of times—to produce a new ...
Regular languages are commonly used to define search patterns and the lexical structure of programming languages. For example, the regular language = {| >} is generated by the Type-3 grammar = ({}, {,},,) with the productions being the following. S → aS S → a
Formally, given examples of strings in a regular language, and perhaps also given examples of strings not in that regular language, it is possible to induce a grammar for the language, i.e., a regular expression that generates that language. Not all regular languages can be induced in this way (see language identification in the limit), but ...
Given a set of strings (also called "positive examples"), the task of regular language induction is to come up with a regular expression that denotes a set containing all of them. As an example, given {1, 10, 100}, a "natural" description could be the regular expression 1⋅0 * , corresponding to the informal characterization " a 1 followed by ...
Today Dorman says 44% of languages have grammatical gender systems, which can help ease communication for people speaking and understanding a language. "Grammatical gender is a classification ...
Similar to other languages, words in Pingelapese can take different forms to add to or even change its meaning. Verbal suffixes are morphemes added at the end of a word to change its form. Prefixes are those that are added at the front. For example, the Pingelapese suffix –kin means 'with' or 'at.' It is added at the end of a verb.