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On the power of 1-tape off-line ATMs running in a bounded number of reversals

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Abstract

It is known that 1-tape-1-counter alternating Turing machines (ATMs) making a constant number of reversals recognize all recursively enumerable languages. Yamamoto and Noguchi raised the question whether 1-tape off-line ATMs with a constant reversal bound have the same computational power. Recently, Jiang has given a negative answer to this question by defining a recursive functionh(s,r,n) such that, for everys-state 1-tape off-line ATMM running inr reversals, the language accepted byM is inASPACE(h(s, r, n)). In this paper we continue the investigation of the reversal complexity of 1-tape off-line ATMs. We improve the result of Jiang showing that the functionh can be reduced to a functionf(s, r, n)≈ log log log logh(s,r,n). We also prove that 1-tape off-line ATMs recognize only recursive languages even if an arbitrary recursive bound (instead of only a constant) on the number of reversals is set. We conclude the paper by giving an astonishing reversal hierarchy theorem for the machines considered.

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Authors and Affiliations

  1. Instytut Informatyki, Uniwersytet Wroclawski, Przesmyckiego 20, 51-151, Wroclaw, Poland

    M. Liśkiewicz

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  1. M. Liśkiewicz
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This research was supported by the Alexander-von-Humboldt-Stiftung while the author was visiting the Institut für Theoretische Informatik, TH Darmstadt, 6100 Darmstadt, Germany.

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Liśkiewicz, M. On the power of 1-tape off-line ATMs running in a bounded number of reversals. Math. Systems Theory 28, 329–339 (1995). https://doi.org/10.1007/BF01185400

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  • DOI: https://doi.org/10.1007/BF01185400

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