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Algebraic laws for regular expressions can be obtained using a method by Gischer which is best explained along an example: In order to check whether (X+Y) * and (X * Y *) * denote the same regular language, for all regular expressions X, Y, it is necessary and sufficient to check whether the particular regular expressions (a+b) * and (a * b ...
In theoretical computer science and formal language theory, a regular language (also called a rational language) [1] [2] 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 expression engines, which are augmented with features that allow the recognition of non-regular languages).
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 ...
For every long enough string in a regular language, there must be a middle section (y) that can be repeated (or pumped) any number of times to produce a string still in the language. In the theory of formal languages, the pumping lemma for regular languages is a lemma that describes an essential property of all regular languages.
Some authors call this type of grammar a right-regular grammar (or right-linear grammar) [1] and the type above a strictly right-regular grammar (or strictly right-linear grammar). [2] An extended left-regular grammar is one in which all rules obey one of A → w, where A is a non-terminal in N and w is in Σ * A → Bw, where A and B are in N ...
A language can have different equivalent grammars, such as equivalent regular expressions (at the lexical levels), or different phrase rules which generate the same language. Using a broader category of grammars, such as LR grammars, can allow shorter or simpler grammars compared with more restricted categories, such as LL grammar, which may ...
Here, is the special regular expression denoting the empty set and ε the special one denoting the empty word; E and F are arbitrary regular expressions. The star height h ( L ) of a regular language L is defined as the minimum star height among all regular expressions representing L .
To decide whether two given regular expressions describe the same language, each can be converted into an equivalent minimal deterministic finite automaton via Thompson's construction, powerset construction, and DFA minimization. If, and only if, the resulting automata agree up to renaming of states, the regular expressions' languages agree.