TY - JOUR
T1 - Inferring regular languages and ω-languages
AU - Fisman, Dana
N1 - Funding Information: I would like to thank Dana Angluin for fascinating discussions on the underlying topics, and the reviewers for their thorough review and insightful questions, that greatly increased the quality of this paper. This research was supported by the United States–Israel Binational Science Foundation ( BSF ) grant 2016239 . Publisher Copyright: © 2018 Elsevier Inc.
PY - 2018/8/1
Y1 - 2018/8/1
N2 - In 1987 Angluin proposed an algorithm, termed L⁎ for inferring an unknown regular language using membership and equivalence queries. This algorithm has found many applications, amongst which in the area of system design and verification. These applications challenge the state-of-the art solutions in various directions, in particular, scaling or working with more succinct representations, and dealing with ω-languages, the main model for reasoning about reactive systems. Both extensions confront a similar difficulty. Inference algorithms typically rely on the correspondence between the automata states and the right congruence, henceforth, the residuality property. DFAs enjoy the residuality property (as stated by the Myhill–Nerode Theorem) but more succinct representations such as non-deterministic and alternating finite automata (NFAs and AFAs) in general do not. The situation in the ω-languages realm is even worse, since none of the traditional automata that can express all regular ω-languages enjoys the residuality property. This paper surveys residual models for regular languages and ω-languages and the learning algorithms that can infer these models.
AB - In 1987 Angluin proposed an algorithm, termed L⁎ for inferring an unknown regular language using membership and equivalence queries. This algorithm has found many applications, amongst which in the area of system design and verification. These applications challenge the state-of-the art solutions in various directions, in particular, scaling or working with more succinct representations, and dealing with ω-languages, the main model for reasoning about reactive systems. Both extensions confront a similar difficulty. Inference algorithms typically rely on the correspondence between the automata states and the right congruence, henceforth, the residuality property. DFAs enjoy the residuality property (as stated by the Myhill–Nerode Theorem) but more succinct representations such as non-deterministic and alternating finite automata (NFAs and AFAs) in general do not. The situation in the ω-languages realm is even worse, since none of the traditional automata that can express all regular ω-languages enjoys the residuality property. This paper surveys residual models for regular languages and ω-languages and the learning algorithms that can infer these models.
KW - Grammatical inference
KW - Model learning
KW - Myhill–Nerode theorem
KW - Regular languages
KW - Right congruence
KW - ω-regular languages
UR - http://www.scopus.com/inward/record.url?scp=85056289807&partnerID=8YFLogxK
U2 - https://doi.org/10.1016/j.jlamp.2018.03.002
DO - https://doi.org/10.1016/j.jlamp.2018.03.002
M3 - Article
SN - 2352-2208
VL - 98
SP - 27
EP - 49
JO - Journal of Logical and Algebraic Methods in Programming
JF - Journal of Logical and Algebraic Methods in Programming
ER -