On polynomial-time bounded truth-table reducibility of NP sets to sparse sets
SIAM Journal on Computing
A uniform approach to define complexity classes
Theoretical Computer Science
On reductions of NP sets to sparse sets
Journal of Computer and System Sciences
More on BPP and the polynomial-time hierarchy
Information Processing Letters
Logspace and logtime leaf languages
Information and Computation
Sparse sets versus complexity classes
Complexity theory retrospective II
Symmetric alternation captures BPP
Computational Complexity
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
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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 Σ$^{P}_{\rm 2}$ cannot have polylog-sparse hard sets under those balanced truth-table- and Turing-bit-reductions, if the polynomial-time hierarchy is infinite.