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Given a regular expression $R$ and a string $Q$, the regular expressionparsing problem is to determine if $Q$ matches $R$ and if so, determine how itmatches, e.g., by a mapping of the characters of $Q$ to the characters in $R$.Regular expression parsing makes finding matches of a regular expression evenmore useful by allowing us to directly extract subpatterns of the match, e.g.,for extracting IP-addresses from internet traffic analysis or extractingsubparts of genomes from genetic data bases. We present a new generaltechniques for efficiently converting a large class of algorithms thatdetermine if a string $Q$ matches regular expression $R$ into algorithms thatcan construct a corresponding mapping. As a consequence, we obtain the firstefficient linear space solutions for regular expression parsing.

From Regular Expression Matching to Parsing