Recognition time of context-free languages by on-line Turing machines

Abstract

It is known that any context-free language can be recognized in time n3 on a “random access machine” or on an on-line or off-line Turing machine. A context-free language which requires n2/(log n)2 steps to be recognized on an on-line Turing machine is known. The principal result of the present paper is to exhibit a context-free language which requires more than n2/log n steps for recognition on an on-line Turing machine. Thus the gap between the upper and lower bound has been reduced. Moreover, it is known that the time required to recognize a linear context-free language is at most n2. Since our example is linear, we now have an example which shows that the upper and lower bounds are close.