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  2. Regular expression - Wikipedia

    en.wikipedia.org/wiki/Regular_expression

    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 ...

  3. Kleene's algorithm - Wikipedia

    en.wikipedia.org/wiki/Kleene's_algorithm

    After that, in each step the expressions R k ij are computed from the previous ones by R k ij = R k-1 ik (R k-1 kk) * R k-1 kj | R k-1 ij. Another way to understand the operation of the algorithm is as an "elimination method", where the states from 0 to n are successively removed: when state k is removed, the regular expression R k-1

  4. Induction of regular languages - Wikipedia

    en.wikipedia.org/wiki/Induction_of_regular_languages

    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 ...

  5. Thompson's construction - Wikipedia

    en.wikipedia.org/wiki/Thompson's_construction

    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.

  6. Brzozowski derivative - Wikipedia

    en.wikipedia.org/wiki/Brzozowski_derivative

    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 ...

  7. Regular language - Wikipedia

    en.wikipedia.org/wiki/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 that allow the recognition of non-regular languages).

  8. Ambiguous grammar - Wikipedia

    en.wikipedia.org/wiki/Ambiguous_grammar

    The regular language of unary strings of a given character, say 'a' (the regular expression a*), has the unambiguous grammar: A → aA | ε …but also has the ambiguous grammar: A → aA | Aa | ε. These correspond to producing a right-associative tree (for the unambiguous grammar) or allowing both left- and right- association. This is ...

  9. Comparison of regular expression engines - Wikipedia

    en.wikipedia.org/wiki/Comparison_of_regular...

    The primary regex crate does not allow look-around expressions. There is an Oniguruma binding called onig that does. SAP ABAP: SAP.com: Proprietary: Tcl: tcl.tk: Tcl/Tk License (BSD-style) Tcl library doubles as a regular expression library. Wolfram Language: Wolfram Research: Proprietary: usable for free on a limited scale on the Wolfram ...