R69-23 The Reduction of Tape Reversals for Off-Line One-Tape Turing Machines

Recently there has been a great deal of study of measures of computational complexity. In light of the results of Blum [1] yielding speedup theorems for abstract complexity measures, and the lack of any general agreement as to reasonable complexity measures, there is reason to study even artificial complexity measures, such as the number of tape reversals on a one-tape Turing machine, which lack intuitive appeal but do lead to some amusing results. The present paper, which should be read in connection with [2], provides the usual Hartmanis-Stearnstype speedup theorem [3] for off-line one-tape Turing machines; namely, the appropriate reversal complexity classes associated with f(x) and cf(x) are the same for any constant c>0. The proofs are based on straightforward applications of the notion of crossing sequences [4].