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: "the join levels of the trotter weil hierarchy are decidable"
  Abstract: The variety DA of finite monoids has a huge number of different characterizations, ranging from two-variable first-order logic FO^2 to unambiguous polynomials. In order to study the structure of the subvarieties of DA, Trotter and Weil considered the intersection of varieties of finite monoids with bands, i.e., with idempotent monoids. The varieties of idempotent monoids are very well understood and fully classified. Trotter and Weil showed that for every band variety V there exists a unique maximal variety W inside DA such that the intersection with bands yields the given band variety V. These maximal varieties W define the Trotter-Weil hierarchy. This hierarchy is infinite and it exhausts DA; induced by band varieties, it naturally has a zigzag shape. In their paper, Trotter and Weil have shown that the corners and the intersection levels of this hierarchy are decidable. #R##N#In this paper, we give a single identity of omega-terms for every join level of the Trotter-Weil hierarchy; this yields decidability. Moreover, we show that the join levels and the subsequent intersection levels do not coincide. Almeida and Azevedo have shown that the join of R-trivial and L-trivial finite monoids is decidable; this is the first non-trivial join level of the Trotter-Weil hierarchy. We extend this result to the other join levels of the Trotter-Weil hierarchy. At the end of the paper, we give two applications. First, we show that the hierarchy of deterministic and codeterministic products is decidable. And second, we show that the direction alternation depth of unambiguous interval logic is decidable.

Connected through hyperedge HE-1 (induced by source paper "the word problem for omega terms over the trotter weil hierarchy"):
  with members:
    - "the separation problem for regular languages by piecewise testable languages"
    - "separating regular languages by piecewise testable and unambiguous languages"
    - "ehrenfeucht fraisse games on omega terms"
    - "on logical hierarchies withinfoâ definable languages"
    - "the fo2 alternation hierarchy is decidable"
    - "representations of stream processors using nested fixed points"
    - "structure theorem and strict alternation hierarchy for fo2 on words"

Connected through hyperedge HE-2 (induced by source paper "one quantifier alternation in first order logic with modular predicates"):
  with members:
    - "lattices of logical fragments over words"
    - "on logical hierarchies withinfoâ definable languages"

Connected through hyperedge HE-3 (induced by source paper "the fo2 alternation hierarchy is decidable"):
  with members:
    - "lattices of logical fragments over words"
    - "languages of dot depth one over infinite words"
    - "an introduction to finite automata and their connection to logic"
    - "on fo 2 quantifier alternation over words"
    - "structure theorem and strict alternation hierarchy for fo2 on words"
    - "logic meets algebra the case of regular languages"

Connected through hyperedge HE-4 (induced by source paper "quantifier alternation in two variable first order logic with successor is decidable"):
  with members:
    - "lattices of logical fragments over words"
    - "the fo2 alternation hierarchy is decidable"
    - "around dot depth one"
    - "structure theorem and strict alternation hierarchy for fo2 on words"

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.FL(Formal Languages and Automata Theory)