Tape-reversal bounded turing machine computations

J. Hartmanis
1968 Journal of computer and system sciences (Print)  
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
more » ... classes. These differences are discussed, and several relations between the different complexity measures and languages are established. I. INTRODUCTION Recent work in automata theory has discussed several computational complexity measures and shown that the quantitative aspects of computation can be submitted to a rigorous mathematical analysis [1]-~[7]~ Furthermore, this initial work on computational complexity has stimulated a more quantitative approach to other parts of automata theory and has given several measures against which to compare the computational power of automata. For example, recent work has established bounds on the memory and time required for the recognition of context-free languages and has characterized the computational power of certain stack automata in terms of memory-bounded Turing-machine computations [8]- [11] . The same approach has been applied to the study of the complexity of decision problems, and has raised several interesting problems about the recognition of the set of primes by memory-bounded automata [12]-[14]. In this paper we continue the study of computational complexity by investigating a complexity measure based on the number of tape reversals which are required to perform the computation on an on-line Tufmg machine. This measure yields a rich hierachy of tape-reversal complexity classes and their properties and ordering are investigated. The most striking difference between this
doi:10.1016/s0022-0000(68)80027-3 fatcat:y3zt6ozcindsrk77krw2exwgsi