On non-determinancy in simple computing devices

SummaryThis paper studies one-tape Turing machines with k read-only heads which are restricted to the original input. The main result shows that if any set accepted by such a 3-head non-deterministic Turing machine can be accepted by a deterministic Turing machine with more read-only heads, then the deterministic and non-deterministic context-sensitive languages are identical. Several related results are derived and some tantalizing open problems are discussed.