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
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