## Computing with Restricted Nondeterminism: The Dependence of the OBDD Size on the Number of Nondeterministic Variables (1999)

Venue: | In Proceedings of the 19th Conference on Foundations of Software Technology and Theoretical Computer Science |

Citations: | 2 - 0 self |

### BibTeX

@INPROCEEDINGS{Sauerhoff99computingwith,

author = {Martin Sauerhoff},

title = {Computing with Restricted Nondeterminism: The Dependence of the OBDD Size on the Number of Nondeterministic Variables},

booktitle = {In Proceedings of the 19th Conference on Foundations of Software Technology and Theoretical Computer Science},

year = {1999},

pages = {342--355}

}

### OpenURL

### Abstract

. It is well-known that an arbitrary nondeterministic Turing machine can be simulated with polynomial overhead 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 nondeterministic OBDDs. If we require that all nondeterministic variables are tested at the top of the OBDD, i. e., at the beginning of the computation, this may blow-up the size exponentially. This is a consequence of the following main result of the paper. There is a sequence of Boolean functions fn : {0, 1} n # {0, 1} such that fn has nondeterministic OBDDs of polynomial size with O(n 1/3 log n) nondeterministic variables, but fn requires exponential size if only at most O(log n) nondeterministic variables may be used. 1 Introduction and Definitions So far, there are only few models of computation for which it has been possible to analyze the power of nondete...

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