On two-way multihead automata

  • Authors:

  • Oscar H. Ibarra

  • Affiliations:

  • -

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 1973

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Abstract

For each positive integer n, let @?^N(n) be the class of sets accepted by a family of automata of type N, each with a read-only input with endmarkers and n two-way input heads. The following result, which is applicable to most types of two-way multihead devices, is proved: If for each positive integer n, there is some integer M"nn such that @?^N(n) is properly contained in @?^N(M^n), then @?^N(n) is properly contained in @?^N(n + c^N) for each n, where c"N=1 or 2, depending on the type of the device. As a consequence, it is shown that deterministic two-way finite automata with n+2 heads are strictly more powerful than deterministic two-way finite automata with n heads for each positive integer n. It is also shown that the class of sets accepted by deterministic (nondeterministic) two-way pushdown automata with n heads is properly included in the class of sets accepted by deterministic (nondeterministic) two-way pushdown automata with n+1 heads.