Guess-and-verify versus unrestricted nondeterminism for OBDDs and one-way Turing machines

Martin Sauerhoff
2003 Journal of computer and system sciences (Print)  
It is well known that a nondeterministic Turing machine can be simulated in polynomial time by a so-called guess-and-verify machine. It is an open question whether an analogous simulation exists in the context of space-bounded computation. In this paper, a negative answer to this question is given for ordered binary decision diagrams (OBDDs) and one-way Turing machines. If it is required that all nondeterministic guesses occur at the beginning of the computation, this can blow up the space
more » ... exity exponentially in the input length for these models. This is a consequence of the following main result of the paper. There is a sequence of boolean functions f n : f0; 1g n -f0; 1g such that f n has nondeterministic OBDDs of polynomial size that use at most ð1=3Þ Á ðn=3Þ 1=3 log n Á ð1 þ oð1ÞÞ nondeterministic guesses for each computation, but f n already requires exponential size if only at most ð1 À eÞ Á ð1=3Þ Á ðn=3Þ 1=3 log n nondeterministic guesses may be used, where e40 is an arbitrarily small constant. r
doi:10.1016/s0022-0000(03)00037-0 fatcat:vtv33exhxzhvzpei343pruvnue