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 Crepe, the first ZK protocol for encoding regular expression equivalence proofs and also the first ZK protocol to target a PSPACE-complete problem. Crepe 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 Crepe on a suite of hundreds of regular expression equivalence proofs. Crepe can validate large proofs in only a few seconds each.
View on arXiv@article{kolesar2025_2504.01198,
title={ Coinductive Proofs of Regular Expression Equivalence in Zero Knowledge },
author={ John Kolesar and Shan Ali and Timos Antonopoulos and Ruzica Piskac },
journal={arXiv preprint arXiv:2504.01198},
year={ 2025 }
}