Certifying DFA Bounds for Recognition and Separation

Orna Kupferman; Nir Lavee; Salomon Sickert

doi:10.1007/978-3-030-88885-5_4

Certifying DFA Bounds for Recognition and Separation

Orna Kupferman, Nir Lavee, Salomon Sickert^*

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-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 language	English
Title of host publication	Automated Technology for Verification and Analysis - 19th International Symposium, ATVA 2021, Proceedings
Editors	Zhe Hou, Vijay Ganesh
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	48-64
Number of pages	17
ISBN (Print)	9783030888848
DOIs	https://doi.org/10.1007/978-3-030-88885-5_4
State	Published - 2021
Event	19th International Symposium on Automated Technology for Verification and Analysis, ATVA 2021 - Virtual, Online Duration: 18 Oct 2021 → 22 Oct 2021

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12971 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	19th International Symposium on Automated Technology for Verification and Analysis, ATVA 2021
City	Virtual, Online
Period	18/10/21 → 22/10/21

Bibliographical note

Publisher Copyright:
© 2021, Springer Nature Switzerland AG.

Access to Document

10.1007/978-3-030-88885-5_4

Cite this

Kupferman, O., Lavee, N., & Sickert, S. (2021). Certifying DFA Bounds for Recognition and Separation. In Z. Hou, & V. Ganesh (Eds.), Automated Technology for Verification and Analysis - 19th International Symposium, ATVA 2021, Proceedings (pp. 48-64). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12971 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-88885-5_4

Kupferman, Orna ; Lavee, Nir ; Sickert, Salomon. / Certifying DFA Bounds for Recognition and Separation. Automated Technology for Verification and Analysis - 19th International Symposium, ATVA 2021, Proceedings. editor / Zhe Hou ; Vijay Ganesh. Springer Science and Business Media Deutschland GmbH, 2021. pp. 48-64 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Kupferman, O, Lavee, N & Sickert, S 2021, Certifying DFA Bounds for Recognition and Separation. in Z Hou & V Ganesh (eds), Automated Technology for Verification and Analysis - 19th International Symposium, ATVA 2021, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12971 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 48-64, 19th International Symposium on Automated Technology for Verification and Analysis, ATVA 2021, Virtual, Online, 18/10/21. https://doi.org/10.1007/978-3-030-88885-5_4

Certifying DFA Bounds for Recognition and Separation. / Kupferman, Orna; Lavee, Nir; Sickert, Salomon.
Automated Technology for Verification and Analysis - 19th International Symposium, ATVA 2021, Proceedings. ed. / Zhe Hou; Vijay Ganesh. Springer Science and Business Media Deutschland GmbH, 2021. p. 48-64 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12971 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Kupferman O, Lavee N, Sickert S. Certifying DFA Bounds for Recognition and Separation. In Hou Z, Ganesh V, editors, Automated Technology for Verification and Analysis - 19th International Symposium, ATVA 2021, Proceedings. Springer Science and Business Media Deutschland GmbH. 2021. p. 48-64. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-88885-5_4

Certifying DFA Bounds for Recognition and Separation

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