On Small Hard Leaf Languages [chapter]

Falk Unger
2005 Lecture Notes in Computer Science  
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 N P ⊆ BLeaf P (A) cannot be polylog-sparse (i.e. censusA ∈ O(log O(1) )), unless P H collapses. We also generalize balanced ≤ P,bit m -reductions, which were introduced in [6], to other bit-reductions, for example (balanced)
more » ... uth-table-and Turing-bit-reductions. Then, similarly to above, we prove that N P and Σ P 2 cannot have polylog-sparse hard sets under those balanced truthtable-and Turing-bit-reductions, if the polynomial-time hierarchy is infinite.
doi:10.1007/11549345_67 fatcat:q2mbj7yiazfinmubwf2heyx3wq