Two-Way Automata and One-Tape Machines: Read Only Versus Linear Time

It is well-known that one-tape Turing machines working in linear time are no more powerful than finite automata, namely they recognize exactly the class of regular languages. We study the costs, in terms of description sizes, of the conversion of nondeterministic finite automata into equivalent linear-time one-tape deterministic machines. We prove a polynomial blowup from two-way nondeterministic finite automata into equivalent weight-reducing one-tape deterministic machines that work in linear time. The blowup remains polynomial if the tape in the resulting machines is restricted to the portion which initially contains the input. However, in this case the machines resulting from our construction are not weight reducing, unless the input alphabet is unary.