### Abstract

In this Letter, we investigate a special distribution, called eigen-distribution, on random assignments for a class of game trees T_{2}^{k}. There are two cases, where the assignments to leaves are independently distributed (ID) and correlated distributed (CD). In the ID case, we prove that the distributional probability ρ{variant} belongs to [frac(sqrt(7) - 1, 3), frac(sqrt(5) - 1, 2)], and ρ{variant} is a strictly increasing function on rounds k ∈ [1, ∞). In the CD case, we propose a reverse assigning technique (RAT) to form two particular sets of assignments, 1-set and 0-set, then show that the E^{1}-distribution (namely, a particular distribution on the assignments of 1-set such that all the deterministic algorithms have the same complexity) is the unique eigen-distribution for T_{2}^{k} in the global distribution.

Original language | English |
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Pages (from-to) | 73-77 |

Number of pages | 5 |

Journal | Information Processing Letters |

Volume | 104 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2007 Oct 16 |

### Keywords

- Computational complexity
- Distributional complexity
- Eigen-distribution
- Game tree
- Randomized algorithms

### ASJC Scopus subject areas

- Theoretical Computer Science
- Signal Processing
- Information Systems
- Computer Science Applications

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## Cite this

*Information Processing Letters*,

*104*(2), 73-77. https://doi.org/10.1016/j.ipl.2007.05.008