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 "bounds for the quantifier depth in finite variable logics alternation hierarchy"):
  Abstract: Given two structures $G$ and $H$ distinguishable in $\fo k$ (first-order logic with $k$ variables), let $A^k(G,H)$ denote the minimum alternation depth of a $\fo k$ formula distinguishing $G$ from $H$. Let $A^k(n)$ be the maximum value of $A^k(G,H)$ over $n$-element structures. We prove the strictness of the quantifier alternation hierarchy of $\fo 2$ in a strong quantitative form, namely $A^2(n)\ge n/8-2$, which is tight up to a constant factor. For each $k\ge2$, it holds that $A^k(n)>\log_{k+1}n-2$ even over colored trees, which is also tight up to a constant factor if $k\ge3$. For $k\ge 3$ the last lower bound holds also over uncolored trees, while the alternation hierarchy of $\fo 2$ collapses even over all uncolored graphs. #R##N#We also show examples of colored graphs $G$ and $H$ on $n$ vertices that can be distinguished in $\fo 2$ much more succinctly if the alternation number is increased just by one: while in $\Sigma_{i}$ it is possible to distinguish $G$ from $H$ with bounded quantifier depth, in $\Pi_{i}$ this requires quantifier depth $\Omega(n^2)$. The quadratic lower bound is best possible here because, if $G$ and $H$ can be distinguished in $\fo k$ with $i$ quantifier alternations, this can be done with quantifier depth $n^{2k-2}$.

Includes members:
  Member "on the speed of constraint propagation and the time complexity of arc consistency testing":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "the propagation depth of local consistency")
  Member "structure theorem and strict alternation hierarchy for fo2 on words":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "two variable logics with some betweenness relations expressiveness satisfiability and membership")

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.LO(Logic in Computer Science)