Abstract
It is well known that the membership question for the smallest hyper-AFL is NP-complete. One may ask whether this is the case for the smallest hyper(1)-AFL, too. Thus we study the family of block-indexed languages. We show that this family is a hyper(1)-AFL which is not a hyper-AFL and that it is contained in the family of languages log(n)-tape reducible to the context-free languages. This implies that the family of block-indexed languages, together with the smallest hyper(1)-AFL, has a tractable membership question and tape complexity log2(n). Finally we note that the set {ww / we {a, b}*} is not a block-indexed language.
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