A leaf-size hierarchy of alternating rebound Turing machines

  • Authors:

  • Lan Zhang;Katsushi Inoue;Akira Ito;Yue Wang

  • Affiliations:

  • Department of Computer Science and Systems Engineering, Yamaguchi University, Ube, 755-8611 Japan;Department of Computer Science and Systems Engineering, Yamaguchi University, Ube, 755-8611 Japan;Department of Computer Science and Systems Engineering, Yamaguchi University, Ube, 755-8611 Japan;Department of Computer Science and Systems Engineering, Yamaguchi University, Ube, 755-8611 Japan

  • Venue:
  • Journal of Automata, Languages and Combinatorics
  • Year:
  • 2002

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Abstract

This paper continues the investigation of the fundamental properties of alternating rebound Turing machines (ARTM's). In particular, we shall introduce a simple, natural complexity measure for ARTM's, called "leaf-size", and provide a hierarchy of complexity classes based on leaf-size bounded computations. Leaf-size, in a sense, reflects the number of processors which run in parallel in reading a given input.We show that for any positive integer k ≥ 1 and for any two functions L : N → N ∪ {0} and L' : N → N ∪ {0} such that (i) L is space constructible by a deterministic rebound Turing machine, (ii) L(n)k+1 = o(log n), and (iii) L'(n) = o(L(n)), there exists a language accepted by a strongly L(n) space-bounded and L(n)k leaf-size bounded ARTM, but not accepted by any weakly L(n) space-bounded and L'(n)k leaf-size bounded ARTM.We further show that for any positive integer k ≥ 1, there exists a language accepted by a 2k + 4 leaf-size bounded alternating rebound automaton, but not accepted by any weakly o(log n) space-bounded and k leaf-size bounded ARTM.