A characterization of two-way deterministic of classes languages
Alfred V. Aho, Jeffrey David Ullman · 1969
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 GSM's that move two ways on the input. Hence, the context sensitive languages and various time and tape complexity classes are equivalent to classes of 2DBA.