Certifying DFA Bounds for Recognition and Separation

Orna Kupferman, Nir Lavee, Salomon Sickert*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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 L and a bound k, recognizability of L by a DFA with k 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.

Original languageAmerican English
Title of host publicationAutomated Technology for Verification and Analysis - 19th International Symposium, ATVA 2021, Proceedings
EditorsZhe Hou, Vijay Ganesh
PublisherSpringer Science and Business Media Deutschland GmbH
Pages48-64
Number of pages17
ISBN (Print)9783030888848
DOIs
StatePublished - 2021
Event19th International Symposium on Automated Technology for Verification and Analysis, ATVA 2021 - Virtual, Online
Duration: 18 Oct 202122 Oct 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12971 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference19th International Symposium on Automated Technology for Verification and Analysis, ATVA 2021
CityVirtual, Online
Period18/10/2122/10/21

Bibliographical note

Publisher Copyright:
© 2021, Springer Nature Switzerland AG.

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