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Prove and Optimize

Prove patterns equivalent, read proven facts about what they match, optimize them safely and find ReDoS risks.

Pattern Algebra and EquivalenceProve that two patterns match the same strings, find the shortest counterexample when they do not, and build intersections, differences and unions.
Language FactsProve the length bounds, required prefix and suffix that every accepted string shares, and use them for indexes and prefilters.
Verified OptimizerRewrite a pattern into a shorter one with identical .NET match behavior, with every rewrite checked and, for regular patterns, proven.
ReDoS Safety AnalysisFind catastrophic backtracking before it reaches production, prove it with a timed attack, and fix it with possessive quantifiers, atomic groups, timeouts or the non-backtracking engine.