Can PCRE Handle Context-Sensitive Grammars like {anbncn; n>0}?

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Enhancing Regular Expressions: Parsing Context-Sensitive Grammars Using PCRE

Regular expression implementations like PCRE exhibit remarkable capabilities beyond traditional context-free grammars. A prime example is the ability to parse the context-free grammar {aⁿbⁿ; n>0}. However, the question arises: can PCRE even handle more complex context-sensitive grammars such as {aⁿbⁿcⁿ; n>0}?

A Solution

Based on a previous attempt and subsequent enhancements, a solution has been discovered:

$regex = '~^
    (?=(a(?-1)?b)c)
     a+(b(?-1)?c)
$~x';

Understanding the Solution

Stripping away the lookahead assertion, the regex checks for an arbitrary number of 'a's followed by an equal number of 'b's and 'c's. The lookahead assertion, (?=(a(?-1)?b)c), ensures that the number of 'a's matches the number of 'b's.

Implications

This solution demonstrates that PCRE can extend its reach beyond non-regular grammars and even reach into the realm of non-context-free grammars. This refutes the common misconception that regular expressions are inherently limited in their parsing capabilities.

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