A note on some simultaneous relations among time, space, and reversal for single work tape nondeterministic turing machines

Abstract

Simultaneous resource bounded complexity classes for nondeterministic single worktape off-line Turing machines are considered such as time-space bounded classes, denoted by NTISP 1 ( T, S ), reversal-space bounded classes, denoted by NRESP 1 ( R, S ), and time-reversal bounded classes, denoted by NTIRE 1 ( T, R ). It is shown that NRESP 1 ( R ( n ), S ( n )) contains NTISP 1 ( S ( n ), R ( n )) and is contained in NTISP 1 ( R ( n ) S ( n ) n 2 log n , R ( n ) log n ). The following corollaries follow: (1) the affirmative solution to the nondeterministic single worktape version of the NC = ? SC problem, NTIRE 1 (poly, polylog) = NTISP 1 (poly, polylog), and (2) a reversal-space trade-off, NRESP 1 (polylog, poly) = NRESP 1 (poly, polylog).