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Restricted Turing Machines and Language Recognition

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Language and Automata Theory and Applications (LATA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9618))

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Abstract

In 1965 Hennie proved that one-tape deterministic Turing machines working in linear time are equivalent to finite automata, namely they characterize regular languages. This result has been improved in different directions, by obtaining optimal lower bounds for the time that one-tape deterministic and nondeterministic Turing machines need to recognize nonregular languages. On the other hand, in 1964 Kuroda showed that one-tape Turing machines that are not allowed to use any extra space, besides the part of the tape which initially contains the input, namely linear bounded automata, recognize exactly context-sensitive languages. In 1967 Hibbard proved that for each integer \(d\ge 2\), one-tape Turing machines that are allowed to rewrite each tape cell only in the first d visits are equivalent to pushdown automata. This gives a characterization of the class of context-free languages in terms of restricted Turing machines. We discuss these and other related models, by presenting an overview of some fundamental results related to them. Descriptional complexity aspects are also considered.

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Notes

  1. 1.

    For technical reasons actually we count the scans from left to right and from right to left on each cell. Hence, each transition reversing the head direction is counted as a double visit.

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Authors and Affiliations

  1. Dipartimento di Informatica, Università degli Studi di Milano, Milano, Italy

    Giovanni Pighizzini

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  1. Giovanni Pighizzini
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Correspondence to Giovanni Pighizzini .

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Editors and Affiliations

  1. Rovira i Virgili University, Tarragona, Spain

    Adrian-Horia Dediu

  2. Czech Technical University, Prague, Czech Republic

    Jan Janoušek

  3. Rovira i Virgili University, Tarragona, Spain

    Carlos Martín-Vide

  4. Justus Liebig University Giessen, Gießen, Germany

    Bianca Truthe

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Pighizzini, G. (2016). Restricted Turing Machines and Language Recognition. In: Dediu, AH., Janoušek, J., Martín-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2016. Lecture Notes in Computer Science(), vol 9618. Springer, Cham. https://doi.org/10.1007/978-3-319-30000-9_3

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  • DOI: https://doi.org/10.1007/978-3-319-30000-9_3

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  • Online ISBN: 978-3-319-30000-9

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