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 / wε {a, b}*} is not a block-indexed language.
This work constitutes part of a Ph. D. thesis and is supported by a German Graduate Fellowship.
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References
Aho, A.V., Hopcroft, J., Ullman, J., The Design and Analysis of Computer Algorithms, Addison Wesley Publishing Company, Massachusetts, 1974.
Albert, J., Über indizierte und m-Block-indizierte Grammatiken, Dissertation, Universität Karlsruhe, 1976.
Asveld, P.R.J., Rational, Algebraic and Hyper-Algebraic Extensions of Families of Languages, Memorandum Nr. 90, Technische Hoogeschool Twente, Onderafdeling der Toegepaste Wiskunde, 1976.
Cook, S.A., Characterization of Pushdown Machines in Terms of Time-Bounded Computers, Journal of the Association for Computing Machinery, 18 (1971) 4–18.
Engelfriet, J., Iterating Iterated Substitution, Memorandum Nr. 143, Technische Hoogeschool Twente, Onderafdeling der Toegepaste Wiskunde, 1976.
Erni, W., Thesis to appear at the Institut für angewandte Informatik und formale Beschreibungsverfahren, Universität Karlsruhe, 1977.
Erni, W., Some Further Languages Log-Tape Reducible to the Context-Free Languages, Research Report of the Institut für angewandte Informatik und formale Beschreibungsverfahren, Universität Karlsruhe, 1976.
Ginsburg, S., Algebraic and Automata-Theoretic Properties of Formal Languages, North-Holland Publishing Company, Amsterdam, 1975.
Leeuwen, J. van, The Membership Question for ETOL-Languages is Polynomially Complete, Information Processing Letters 3 (1975) 138–143.
Rozenberg, G., Salomaa, A., L-Systems, Lecture Notes in Computer Science 15 (1974).
Salomaa, A., Formal Languages, Academic Press, New York, 1973.
Sudborough, I.H., On Languages Log-Tape Reducible to Context-Free Languages, Proceedings of 1976 Conference on Information Sciences and Systems at Johns Hopkins University.
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© 1977 Springer-Verlag Berlin Heidelberg
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Erni, W.J. (1977). On the time and tape complexity of hyper(1)-AFL's. In: Salomaa, A., Steinby, M. (eds) Automata, Languages and Programming. ICALP 1977. Lecture Notes in Computer Science, vol 52. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-08342-1_18
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DOI: https://doi.org/10.1007/3-540-08342-1_18
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