TY - GEN
T1 - Certifying DFA Bounds for Recognition and Separation
AU - Kupferman, Orna
AU - Lavee, Nir
AU - Sickert, Salomon
N1 - Publisher Copyright: © 2021, Springer Nature Switzerland AG.
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85118122347&partnerID=8YFLogxK
U2 - https://doi.org/10.1007/978-3-030-88885-5_4
DO - https://doi.org/10.1007/978-3-030-88885-5_4
M3 - منشور من مؤتمر
SN - 9783030888848
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 48
EP - 64
BT - Automated Technology for Verification and Analysis - 19th International Symposium, ATVA 2021, Proceedings
A2 - Hou, Zhe
A2 - Ganesh, Vijay
PB - Springer Science and Business Media Deutschland GmbH
T2 - 19th International Symposium on Automated Technology for Verification and Analysis, ATVA 2021
Y2 - 18 October 2021 through 22 October 2021
ER -