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 f n : {0, 1}n → {0, 1} such that f n has nondeterministic OBDDs of polynomial size with O(n 1/3 log n) nondeterministic variables, but f n requires exponential size if only at most O(log n) nondeterministic variables may be used.
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Sauerhoff, M. (1999). Computing with Restricted Nondeterminism: The Dependence of the OBDD Size on the Number of Nondeterministic Variables. In: Rangan, C.P., Raman, V., Ramanujam, R. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1999. Lecture Notes in Computer Science, vol 1738. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46691-6_28
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DOI: https://doi.org/10.1007/3-540-46691-6_28
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