Visits, Crosses, and Reversals for Nondeterministic Off-Line Machines

The different concepts involved in "reversal complexity"--counting reversals (sweeps), visits to a square, or crossing sequences--are discussed for nondeterministic off-line Turing machines with one working tape and for preset Turing machines, a generalization of two-way checking automata. Restriction to finite reversals or visits or crosses yields the same family, NSPACE(log2 n), for off-line one working tape Turing machines or for two-way checking automata. For each k, a k-reversal bounded machine has the power of a nondeterministic k-head finite automaton. Finite visit preset Turing machines with working tapes selected from context-free languages yield ~. For an arbitrary bounding function T(n), a T(n) reversal or visit bound on a nondeterministic off-line Turing machine corresponds to a T(n) logs n space bound within a linear factor. However, there is no general linear speedup theorem for reversal bounds on a nondeterministic off-line Turing machine.