It is shown that a class of languages is defined by a class of two-way deterministic balloon automata if and only if that class is closed under marked union, marked Kleene closure and the inverse mappings performed by deterministic GSMs that move two ways on the input. Hence, the context sensitive languages and various time and tape complexity classes are equivalent to classes of two-way deterministic balloon automata. © 1971 Academic Press, Inc.
Aho, A. V., & Ullman, J. D. (1970). A characterization of two-way deterministic classes of languages. Journal of Computer and System Sciences, 4(6), 523–538. https://doi.org/10.1016/S0022-0000(70)80027-7