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

Simultaneous resource bounded complexity classes for nondeterministic single worktape off-line Turing machines are considered such as time-space bounded classes, denoted by NTISP₁(T, S), reversal-space bounded classes, denoted by NRESP₁(R, S), and time-reversal bounded classes, denoted by NTIRE₁(T, R). It is shown that NRESP₁(R(n), S(n)) contains NTISP₁(S(n), R(n)) and is contained in NTISP₁(R(n) S(n)n² 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, NTIRE₁(poly, polylog) = NTISP₁(poly, polylog), and (2) a reversal-space trade-off, NRESP₁(polylog, poly) = NRESP₁(poly, polylog).