Dmitry BerdinskyPhongpitak TrakulditMahidol UniversityCommission on Higher Education2019-08-232019-08-232018-01-01Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol.10792 LNCS, (2018), 245-25716113349030297432-s2.0-85045342054https://repository.li.mahidol.ac.th/handle/20.500.14594/45678© Springer International Publishing AG, part of Springer Nature 2018. In this paper we introduce a way to estimate a level of closeness of Cayley automatic groups to the class of automatic groups using a certain numerical characteristic. We characterize Cayley automatic groups which are not automatic in terms of this numerical characteristic and then study it for the lamplighter group, the Baumslag–Solitar groups and the Heisenberg group.Mahidol UniversityComputer ScienceMathematicsConference PaperSCOPUS10.1007/978-3-319-77313-1_19