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It is shown, that NTAPE(n) is equal to TAPE(n) if and only if every language L¿¿{1}*¿ which is acceptable by a nondeterministic two-way one-counter automaton whose counter length is bounded by the length of its input is contained in TAPE(log n).

The LBA-problem and the deterministic tape complexity of two-way one-counter languages over a one-letter alphabet