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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 .
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:
NFAs are used in the implementation of regular expressions: Thompson's construction is an algorithm for compiling a regular expression to an NFA that can efficiently perform pattern matching on strings. Conversely, Kleene's algorithm can be used to convert an NFA into a regular expression (whose size is generally exponential in the input ...
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.
To simulate the operation of a DFA on a given input string, one needs to keep track of a single state at any time: the state that the automaton will reach after seeing a prefix of the input. In contrast, to simulate an NFA, one needs to keep track of a set of states: all of the states that the automaton could reach after seeing the same prefix ...
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.
For example, the singleton input set {aabbaabb} leads to an automaton corresponding to the regular expression (a + ⋅b +) *. An extension of this approach is the predecessor-successor method which generalizes each character repetition immediately to a Kleene + and then includes for each character the set of its possible predecessors in its state.
RE2 is a software library which implements a regular expression engine. It uses finite-state machines, in contrast to most other regular expression libraries. RE2 supports a C++ interface. RE2 was implemented by Google and Google uses RE2 for Google products. [3]