Zero-knowledge (ZK) protocols enable software developers to provide proofs of their programs’ correctness to other parties without revealing the programs themselves. Regular expressions are pervasive in real-world software, and zero-knowledge protocols have been developed in the past for the problem of checking whether an individual string appears in the language of a regular expression, but no existing protocol addresses the more complex PSPACE-complete problem of proving that two regular expressions are equivalent. We introduce Crêpe , the first ZK protocol for encoding regular expression equivalence proofs and also the first ZK protocol to target a PSPACE-complete problem. Crêpe uses a custom calculus of proof rules based on regular expression derivatives and coinduction, and we introduce a sound and complete algorithm for generating proofs in our format. We test Crêpe on a suite of hundreds of regular expression equivalence proofs. Crêpe can validate large proofs in only a few seconds each.

@article{paperbot3001,
  title = {Coinductive Proofs of Regular Expression Equivalence in Zero Knowledge},
  author = {John C. Kolesar and Shan Ali and Timos Antonopoulos and Ruzica Piskac},
  journal = {Proceedings of the ACM on Programming Languages},
  volume = {9},
  number = {OOPSLA2},
  year = {2025},
  doi = {10.1145/3763063}
}