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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).
Therefore, the length of the regular expression representing the language accepted by M is at most 1 / 3 (4 n+1 (6s+7)f - f - 3) symbols, where f denotes the number of final states. This exponential blowup is inevitable, because there exist families of DFAs for which any equivalent regular expression must be of exponential size.
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 ...
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.
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 ...
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 ...
When a language is given by a regular expression, the concept of derivatives leads to an algorithm for deciding whether a given word belongs to the regular expression. Given a finite alphabet A of symbols, [ 6 ] a generalized regular expression R denotes a possibly infinite set of finite-length strings over the alphabet A , called the language ...