The contiguity in R/M

  • Authors:

  • Zhang Zaiyue;Sui Yuefei

  • Affiliations:

  • Department of Computer Science, Yangzhou University, Jiangsu 225009, P.R. China;Institute of Computing Technology, The Chinese Academy of Sciences, Beijing 100080, P.R. China

  • Venue:
  • Journal of Computer Science and Technology
  • Year:
  • 2002

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Abstract

An r.e. degree c is contiguous if degwtt(A) = degwtt(B) for any r.e. sets A, B ∈ c. In this paper, we generalize the notation of contiguity to the structure R/M, the upper semilattice of the r.e. degree set R modulo the cappable r.e. degree set M. An element [c] ∈ R/M is contiguous if [degwtt(A)] = [degwtt(B)] for any r.e. sets A, B such that degT(A), degT(B) ∈ [c]. It is proved in this paper that every nonzero element in R/M is not contiguous, i.e., for every element [c] ∈ R/M, if [c] ≠ [o] then there exist at least two r.e. sets A, B such that degT(A),degT(B) ∈ [c] and [degwtt(A)] ≠ [degwtt(B)].