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A regular expression (shortened as regex or regexp ), [1] sometimes referred to as rational expression, [2] [3] is a sequence of characters that specifies a match pattern in text. Usually such patterns are used by string-searching algorithms for "find" or "find and replace" operations on strings, or for input validation.
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 arbitrarily many (maybe even none) 0's". However, (0+1) * and 1+(1⋅0)+(1⋅0⋅0) is another regular expression, denoting the largest (assuming Σ = {0,1}) and the smallest set ...
ij is represented by a regular expression; the algorithm computes them step by step for k = -1, 0, ..., n. Since there is no state numbered higher than n, the regular expression R n 0j represents the set of all strings that take M from its start state q 0 to q j. If F = { q 1,...,q f} is the set of accept states, the regular expression R n 01 ...
Regular language. 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 ...
A Kleene algebra is a set A together with two binary operations + : A × A → A and · : A × A → A and one function * : A → A, written as a + b, ab and a* respectively, so that the following axioms are satisfied. Identity elements for + and ·: There exists an element 0 in A such that for all a in A: a + 0 = 0 + a = a.
Thompson's construction. In computer science, Thompson's construction algorithm, also called the McNaughton–Yamada–Thompson algorithm, [1] is a method of transforming a regular expression into an equivalent nondeterministic finite automaton (NFA). [2] This NFA can be used to match strings against the regular expression.
Python has two major implementations, the built in re and the regex library. Ruby 1.8, Ruby 1.9, and Ruby 2.0 and later versions use different engines; Ruby 1.9 integrates Oniguruma, Ruby 2.0 and later integrate Onigmo, a fork from Oniguruma. The primary regex crate does not allow look-around expressions.
If the input did contain an even number of 0s, M will finish in state S 1, an accepting state, so the input string will be accepted. The language recognized by M is the regular language given by the regular expression (1*) (0 (1*) 0 (1*))*, where * is the Kleene star, e.g., 1* denotes any number (possibly zero) of consecutive ones.