k-REWB matching cannot be solved in O(n to the 2k minus epsilon) time under SETH, is W[2]-hard parameterized by expression length, and 2-use 2-REWBs require superlinear time unless triangle detection does; 1-use REWBs admit an O(n log squared n) algorithm.
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A Rocq-mechanized semantics for JavaScript regex with backtracking, proven equivalent to an ECMAScript embedding, then used to verify contextual equivalence of rewrites and to prove correctness of the PikeVM algorithm.
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On the Complexity of the Matching Problem of Regular Expressions with Backreferences
k-REWB matching cannot be solved in O(n to the 2k minus epsilon) time under SETH, is W[2]-hard parameterized by expression length, and 2-use 2-REWBs require superlinear time unless triangle detection does; 1-use REWBs admit an O(n log squared n) algorithm.
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Formal Verification for JavaScript Regular Expressions: a Proven Semantics and its Applications (Extended Version)
A Rocq-mechanized semantics for JavaScript regex with backtracking, proven equivalent to an ECMAScript embedding, then used to verify contextual equivalence of rewrites and to prove correctness of the PikeVM algorithm.