Improved depth lower bounds for small distance connectivity

@article{Beame1998ImprovedDL,
title={Improved depth lower bounds for small distance connectivity},
author={Paul Beame and Russell Impagliazzo and Toniann Pitassi},
journal={computational complexity},
year={1998},
volume={7},
pages={325-345}
}
We consider the problem of determining, given a graph G with specified nodes s and t, whether or not there is a path of at most k edges in G from s to t. We show that solving this problem on polynomialsize unbounded fan-in circuits requires depth $\Omega{\rm(log\,log}\,k)$ , improving on a depth lower bound of $\Omega{\rm(log^*}\,k)$ when $k = {\rm log}^{O(1)}n$ given by Ajtai (1989), Bellantoni et al. (1992). More generally, we obtain an improved size-depth tradeoff lower bound for the… CONTINUE READING

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