Tape-Reversal Bounded Turing Machine Computations

This paper studies the classification of recursive sets by the number of tape reversals required for their recognition on a two-tape Turing machine with a one-way input tape. This measure yields a rich hierarchy of tape-reversal limited complexity classes and their properties and ordering are investigated. The most striking difference between this and the previously studied complexity measures lies in the fact that the "speed-up" theorem does not hold for slowly growing tape-reversal complexity classes. These differences are discussed, and several relations between the different complexity measures and languages are established.