Relationships Between Nondeterministic and Deterministic Tape Complexities

This paper first proves the Savitch Theorem: any nondeterminstic L(n)− tape bounded Turing Machine can be simulated by a deterministic [L(n)]− tape bounded Turing machine, provided L(n) ≥ log2n. Then as an attempt to answer the following question: “Given a nondeterministic tape bounded Turing machine which accepts set A, how much additional storage does a deterministic Turing machine require to recognize A?”, the paper indicates that showing whether there exists any set of strings that is accepted by some nondeterministic Turing machine within storage L(n) and some deterministic Turing machine within storage L(n) is equvilent of showing the set of thread-able maze could be accepted by some deterministic Turing machine within storage L(n) = log2(n).