Certifying DFA Bounds for Recognition and Separation
Abstract
The automation of decision procedures makes certification essential. We suggest to use determinacy of turn-based two-player games with regular winning conditions in order to generate certificates for the number of states that a deterministic finite automaton (DFA) needs in order to recognize a given language. Given a language and a bound , recognizability of by a DFA with states is reduced to a game between Prover and Refuter. The interaction along the game then serves as a certificate. Certificates generated by Prover are minimal DFAs. Certificates generated by Refuter are faulty attempts to define the required DFA. We compare the length of offline certificates, which are generated with no interaction between Prover and Refuter, and online certificates, which are based on such an interaction, and are thus shorter. We show that our approach is useful also for certification of separability of regular languages by a DFA of a given size. Unlike DFA minimization, which can be solved in polynomial time, separation is NP-complete, and thus the certification approach is essential. In addition, we prove NP-completeness of a strict version of separation.
Keywords
Cite
@article{arxiv.2107.01566,
title = {Certifying DFA Bounds for Recognition and Separation},
author = {Orna Kupferman and Nir Lavee and Salomon Sickert},
journal= {arXiv preprint arXiv:2107.01566},
year = {2022}
}
Comments
This is the full version of an article with the same title that appears in the ATVA 2021 conference proceedings. The final authenticated publication is available online at https://doi.org/[not-yet-existing-DOI]