human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "using the no search easy hard technique for downward collapse"):
  Abstract: The top part of the preceding figure [figure appears in actual paper] shows some classes from the (truth-table) bounded-query and boolean hierarchies. It is well-known that if either of these hierarchies collapses at a given level, then all higher levels of that hierarchy collapse to that same level. This is a standard ``upward translation of equality'''' that has been known for over a decade. The issue of whether these hierarchies can translate equality {\em downwards\/} has proven vastly more challenging. In particular, with regard to the figure above, consider the following claim: $$P_{m-tt}^{\Sigma_k^p} = P_{m+1-tt}^{\Sigma_k^p} \implies DIFF_m(\Sigma_k^p) coDIFF_m(\Sigma_k^p) = BH(\Sigma_k^p).~~~~(*)$$ This claim, if true, says that equality translates downwards between levels of the bounded-query hierarchy and the boolean hierarchy levels that (before the fact) are immediately below them. .pp Until recently, it was not known whether~(*) {\em ever\/} held, except for the degenerate cases $m=0$ and $k=0$. Then Hemaspaandra, Hemaspaandra, and Hempel~\cite{hem-hem-hem:j:downward-translation} proved that~(*) holds for all $m$, for $k < 2$. Buhrman and Fortnow~\cite{buh-for:j:two-queries} then showed that, when $k=2$,~($*$) holds for the case $m = 1$. In this paper, we prove that for the case $k=2$,~($*$) holds for all values of $m$. Since there is an oracle relative to which ``for $k=1$,~($*$) holds for all $m$'''' fails~\cite{buh-for:j:two-queries}, our achievement of the $k=2$ case cannot to be strengthened to $k=1$ by any relativizable proof technique. The new downward translation we obtain also tightens the collapse in the polynomial hierarchy implied by a collapse in the bounded-query hierarchy of the second level of the polynomial hierarchy.

Includes members:
  Member "what s up with downward collapse using the easy hard technique to link boolean and polynomial hierarchy collapses":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "a moment of perfect clarity i the parallel census technique")
  Member "a downward collapse within the polynomial hierarchy":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "a moment of perfect clarity i the parallel census technique")

Question: Please tell me which class the source paper belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.CC(Computational Complexity)