On tape-bounded complexity classes and multi-head finite automata

The principal result described in this paper is the equivalence of the following statements: (1) Every set accepted by a nondeterministic one-way two-head finite automaton can be accepted by a deterministic two-way k-head finite automaton, for some k. (2) The context-free language LPΣ (described in the paper) is recognized by a (log n)-tape bounded deterministic Turing machine. (3) Every set accepted by a L(n)-tape bounded nondeterministic Turing machine is recognized by a L(n)-tape bounded deterministic Turing machine, provided L(n) ≥ log n. This work extends results reported earlier by Hartmanis [2], Savitch [9,10], and Lewis, Stearns, and Hartmanis [6].