Abstract

For the recognition of context-free languages (CF-languages), use is made of Turing machines with two tapes: the input tape and the operational tape. Let n be the length of the input tape. As a measure of complexity we choose the length of the operational tape L(n). We denote by M (respectively, N) the class of languages which are recognized on deterministic (nondeterministic) Turing machines with L(n) ~< log2n. It is known that all CF-languages enter in class N [4, 7] and are recognized by deterministic Turing machines with L(n) ~< (log2n) 2 [3], while class M contains certain subclasses of CF-languages (for example, the Dyck language, bounded CFlanguages [7]). It is also noted in [7] that all the examples of CF-languages known to the authors belong to class M. The following two problems are well known:

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