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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.
Let Φ be any abstract measure of computational complexity, and let L denote the specific measure of memory resource (tape) on one tape Turing machines. Denote by Rt( )Φ the class of all total functions whose Φ-complexity is bounded by the function t( ) almost everywhere. Call such classes Φ-complexity classes. We are interested in relationships among these classes, under proper set inclusion (⊂)....
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