On the construction of parallel computers from various bases of Boolean functions
Theoretical Computer Science
Bounded-width polynomial-size branching programs recognize exactly those languages in NC1
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
On polynomial-time bounded truth-table reducibility of NP sets to sparse sets
SIAM Journal on Computing
Journal of the ACM (JACM)
A uniform approach to define complexity classes
Theoretical Computer Science
An introduction to Kolmogorov complexity and its applications
An introduction to Kolmogorov complexity and its applications
More on BPP and the polynomial-time hierarchy
Information Processing Letters
Symmetric alternation captures BPP
Computational Complexity
Competing Provers Yield Improved Karp-Lipton Collapse Results
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Some connections between nonuniform and uniform complexity classes
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
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Unger studied the balanced leaf languages defined via poly-logarithmically sparse leaf pattern sets. Unger shows that NP-complete sets are not polynomial-time many-one reducible to such balanced leaf language unless the polynomial hierarchy collapses to Θ$^{p}_{\rm 2}$ and that Σ$^{p}_{\rm 2}$-complete sets are not polynomial-time bounded-truth-table reducible (respectively), polynomial-time Turing reducible) to any such balanced leaf language unless the polynomial hierarchy collapses to Δ$^{p}_{\rm 2}$ (respectively, Σ$^{p}_{\rm 4}$). This paper studies the complexity of the class of such balanced leaf languages, which will be denoted by VSLL. In particular, the following tight upper and lower bounds of VSLL are shown: 1. coNP ⊆ VSLL ⊆ coNP/poly (the former inclusion is already shown by Unger). 2. coNP/1 $\not\subseteq$ VSLL unless PH = Θ$^{p}_{\rm 2}$. 3. For all constant c0, VSLL $\not\subseteq$ coNP/nc. 4. P/(loglog(n)+O(1))⊆ VSLL. 5. For all h(n) = loglog(n) + ω(1), P$/h \not\subseteq$ VSLL.