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Some classes of regular languages can only be described by deterministic finite automata whose size grows exponentially in the size of the shortest equivalent regular expressions. The standard example here is the languages L k consisting of all strings over the alphabet {a,b} whose kth-from-last letter equals a.
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.
The algorithm works recursively by splitting an expression into its constituent subexpressions, from which the NFA will be constructed using a set of rules. [3] More precisely, from a regular expression E, the obtained automaton A with the transition function Δ [clarification needed] respects the following properties:
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).
We consider two such regular expressions equal if they describe the same language. Then A forms a Kleene algebra. In fact, this is a free Kleene algebra in the sense that any equation among regular expressions follows from the Kleene algebra axioms and is therefore valid in every Kleene algebra. Again let Σ be an alphabet.
Example of Kleene star applied to the empty set: ∅ * = {ε}. Example of Kleene plus applied to the empty set: ∅ + = ∅ ∅ * = { } = ∅, where concatenation is an associative and noncommutative product. Example of Kleene plus and Kleene star applied to the singleton set containing the empty string:
Pages in category "Regular expressions" The following 12 pages are in this category, out of 12 total. This list may not reflect recent changes. ...
MediaWiki's regular expression syntax works like this: Most characters represent themselves. For example, insource:/C-3p0/ will search for pages containing the literal string "C-3p0" (case-sensitive). The following metacharacters are treated specially: . + * ? | { [ ] ( ) " \ # @ < ~. Any metacharacter can be escaped by preceding it with a ...