Space and Reversals Complexity of Nonregular Languages

Alberto Bertoni, Carlo Mereghetti, and Giovanni Pighizzini

Dipartimento di Scienze dell'Informazione
Università degli Studi di Milano
via Comelico 39 -- 20135 Milano, Italy
In this paper, lower bounds on space and input head reversals for deterministic, nondeterministic, and alternating Turing machines accepting nonregular languages are studied. 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 prove 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.

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