Sparse P-Hard Sets Yield Space-Efficient Algorithms

@inproceedings{Ogihara1995SparsePS,
  title={Sparse P-Hard Sets Yield Space-Efficient Algorithms},
  author={Mitsunori Ogihara},
  booktitle={FOCS},
  year={1995}
}
Hartmanis conjectured that there exist no sparse complete sets for P under logspace many-one reductions. In this paper, in support of the conjecture, at as shown that if P has sparse hard sets under logspace many-one reductions, then P E DSPACE[log2n]. The result follows f rom a more general statement: i f P has 2P01Y'0g sparse hard sets under poly-logarithmic space-computable many-one reductions, then P C DSPACE[poZylog] . 

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