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**White pebbles help.**
*(English)*
Zbl 0657.68049

Author’s summary: “It is proved that for infinitely many n there is a directed acyclic graph with vertex indegrees bounded by 2 that has a strategy of the black-white pebble game using n pebbles and for which any strategy of the black pebble game requires \(\Omega\) (n log n/log log n) pebbles. This shows that there is a family of straight-line programs for which nondeterminism reduces the space required to evaluate the programs by more than any constant factor.”

Reviewer: R.Klette

### MSC:

68Q05 | Models of computation (Turing machines, etc.) (MSC2010) |

03D15 | Complexity of computation (including implicit computational complexity) |

68Q45 | Formal languages and automata |

### Keywords:

nondeterministic computations; computational complexity; black-white pebbling; pebble game; straight-line programs
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\textit{R. Wilber}, J. Comput. Syst. Sci. 36, No. 2, 108--124 (1988; Zbl 0657.68049)

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### References:

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