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In theoretical computer science, in particular in formal language theory, Kleene's algorithm transforms a given nondeterministic finite automaton (NFA) into a regular expression. Together with other conversion algorithms, it establishes the equivalence of several description formats for regular languages.
Regular expressions and nondeterministic finite automata are two representations of formal languages. For instance, text processing utilities use regular expressions to describe advanced search patterns, but NFAs are better suited for execution on a computer.
Conversely, Kleene's algorithm can be used to convert an NFA into a regular expression (whose size is generally exponential in the input automaton). NFAs have been generalized in multiple ways, e.g., nondeterministic finite automata with ε-moves , finite-state transducers , pushdown automata , alternating automata , ω-automata , and ...
In the theory of computation, a generalized nondeterministic finite automaton (GNFA), also known as an expression automaton or a generalized nondeterministic finite state machine, is a variation of a nondeterministic finite automaton (NFA) where each transition is labeled with any regular expression. The GNFA reads blocks of symbols from the ...
Arden's rule can be used to help convert some finite automatons to regular expressions, [how?] ... Chapter 2: Finite Automata and Regular Expressions, p.54.
In automata theory (a branch of theoretical computer science), DFA minimization is the task of transforming a given deterministic finite automaton (DFA) into an equivalent DFA that has a minimum number of states. Here, two DFAs are called equivalent if they recognize the same regular language. Several different algorithms accomplishing this ...
It is widely used for regular expressions, which is the context in which it was introduced by Stephen Kleene to characterize certain automata, where it means "zero or more repetitions".
A regular expression may be used to conveniently describe an advanced search pattern in a "find and replace"–like operation of a text processing utility. Glushkov's algorithm can be used to transform it into an NFA, which furthermore is small by nature, as the number of its states equals the number of symbols of the regular expression, plus one.