Greedy Regular Expression Matching

Frisch, Alain; Cardelli, Luca

doi:10.1007/978-3-540-27836-8_53

Cited by 44 publications

(46 citation statements)

References 13 publications

(4 reference statements)

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“…(This is similar to the approach taken by Frisch and Cardelli for GREEDY matching [4], and Sulzmann and Lu for POSIX matching [11]). The string underlying a value can be calculated by the flat function, written | | and defined as:…”

Section: Posix Regular Expression Matchingmentioning

confidence: 76%

“…Sulzmann and Lu sketch in [11] an informal correctness proof: but to us it contains unfillable gaps. 4 Our specification of a POSIX value consists of a simple inductive definition that given a string and a regular expression uniquely determines this value. Derivatives as calculated by Brzozowski's method are usually more complex regular expressions than the initial one; various optimisations are possible.…”

Section: Contributionsmentioning

confidence: 99%

“…In this way the POSIX value is supposed to be the biggest value for a given string and regular expression. Sulzmann and Lu explicitly refer to the paper [4] by Frisch and Cardelli from where they have taken the idea for their correctness proof. Frisch and Cardelli introduced a similar ordering for GREEDY matching and they showed that their GREEDY matching algorithm always produces a maximal element according to this ordering (from all possible solutions).…”

Section: The Correctness Argument By Sulzmann and Lumentioning

confidence: 99%

“…There are two commonly used disambiguation strategies to generate a unique answer: one is called GREEDY matching [4] and the other is POSIX matching [7,11,13]. For example consider the string xy and the regular expression (x + y + xy)…”

Section: Introductionmentioning

confidence: 99%

“…This proof idea is inspired by work of Frisch and Cardelli [4] on a GREEDY regular expression matching algorithm. However, we were not able to establish transitivity and totality for the "order relation" by Sulzmann and Lu.…”

Section: Introductionmentioning

confidence: 99%

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POSIX Lexing with Derivatives of Regular Expressions (Proof Pearl)

Ausaf

Dyckhoff

Urban

2016

Interactive Theorem Proving

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Abstract. Brzozowski introduced the notion of derivatives for regular expressions. They can be used for a very simple regular expression matching algorithm. Sulzmann and Lu cleverly extended this algorithm in order to deal with POSIX matching, which is the underlying disambiguation strategy for regular expressions needed in lexers. Sulzmann and Lu have made available on-line what they call a "rigorous proof" of the correctness of their algorithm w.r.t. their specification; regrettably, it appears to us to have unfillable gaps. In the first part of this paper we give our inductive definition of what a POSIX value is and show (i) that such a value is unique (for given regular expression and string being matched) and (ii) that Sulzmann and Lu's algorithm always generates such a value (provided that the regular expression matches the string). We also prove the correctness of an optimised version of the POSIX matching algorithm. Our definitions and proof are much simpler than those by Sulzmann and Lu and can be easily formalised in Isabelle/HOL. In the second part we analyse the correctness argument by Sulzmann and Lu and explain why the gaps in this argument cannot be filled easily.

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Section: Posix Regular Expression Matchingmentioning

confidence: 76%

Section: Contributionsmentioning

confidence: 99%

Section: The Correctness Argument By Sulzmann and Lumentioning

confidence: 99%