human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "slicewise definability in first order logic with bounded quantifier rank"
  Abstract: For every $q\in \mathbb N$ let $\textrm{FO}_q$ denote the class of sentences of first-order logic FO of quantifier rank at most $q$. If a graph property can be defined in $\textrm{FO}_q$, then it can be decided in time $O(n^q)$. Thus, minimizing $q$ has favorable algorithmic consequences. Many graph properties amount to the existence of a certain set of vertices of size $k$. Usually this can only be expressed by a sentence of quantifier rank at least $k$. We use the color-coding method to demonstrate that some (hyper)graph problems can be defined in $\textrm{FO}_q$ where $q$ is independent of $k$. This property of a graph problem is equivalent to the question of whether the corresponding parameterized problem is in the class $\textrm{para-AC}^0$. #R##N#It is crucial for our results that the FO-sentences have access to built-in addition and multiplication. It is known that then FO corresponds to the circuit complexity class uniform $\textrm{AC}^0$. We explore the connection between the quantifier rank of FO-sentences and the depth of $\textrm{AC}^0$-circuits, and prove that $\textrm{FO}_q \subsetneq \textrm{FO}_{q+1}$ for structures with built-in addition and multiplication.

Connected through hyperedge HE-1 (induced by source paper "on the descriptive complexity of color coding"):
  with members:
    - "computing hitting set kernels by ac 0 circuits"
    - "on the parallel parameterized complexity of the graph isomorphism problem"
    - "fast parallel fixed parameter algorithms via color coding"

Connected through hyperedge HE-2 (induced by source paper "computing hitting set kernels by ac 0 circuits"):
  with members:
    - "computing kernels in parallel lower and upper bounds"
    - "some lower bounds in parameterized rm ac 0"
    - "fast parallel fixed parameter algorithms via color coding"
    - "towards optimal and expressive kernelization for d hitting set"

Question: Please tell me which class the center node 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)