Sciweavers

Share
MFCS
2005
Springer

On Small Hard Leaf Languages

12 years 3 months ago
On Small Hard Leaf Languages
This paper deals with balanced leaf language complexity classes, introduced independently in [1] and [14]. We propose the seed concept for leaf languages, which allows us to give “short” representations for leaf words. We then use seeds to show that leaf languages A with NP ⊆ BLeafP (A) cannot be polylog-sparse (i.e. censusA ∈ O(logO(1) )), unless PH collapses. We also generalize balanced ≤P,bit m -reductions, which were introduced in [6], to other bit-reductions, for example (balanced) truth-table- and Turing-bit-reductions. Then, similarly to above, we prove that NP and ΣP 2 cannot have polylog-sparse hard sets under those balanced truthtable- and Turing-bit-reductions, if the polynomial-time hierarchy is infinite. Keywords Computational Complexity, Leaf Languages, Seeds, Sparseness
Falk Unger
Added 28 Jun 2010
Updated 28 Jun 2010
Type Conference
Year 2005
Where MFCS
Authors Falk Unger
Comments (0)
books