Testing the descriptional power of small Turing machines on nonregular language acceptance

We study lower bounds on space and input head reversals for deterministic, nondeterministic, and alternating Turing machines accepting nonregular languages. Three notions of space, namely strong, middle, weak are considered, and another notion, called accept, is introduced. In all cases, we obtain tight lower bounds. Moreover, we show that, while for determinism and nondeterminism such lower bounds are optimal even with respect to unary languages, for alternation optimal lower bounds for unary languages turn out to be strictly higher than those for languages over alphabets with two or more symbols.