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: "definability of linear equation systems over groups and rings"
  Abstract: Motivated by the quest for a logic for PTIME and recent insights that the#N#descriptive complexity of problems from linear algebra is a crucial aspect of#N#this problem, we study the solvability of linear equation systems over finite#N#groups and rings from the viewpoint of logical (inter-)definability. All#N#problems that we consider are decidable in polynomial time, but not expressible#N#in fixed-point logic with counting. They also provide natural candidates for a#N#separation of polynomial time from rank logics, which extend fixed-point logics#N#by operators for determining the rank of definable matrices and which are#N#sufficient for solvability problems over fields. Based on the structure theory#N#of finite rings, we establish logical reductions among various solvability#N#problems. Our results indicate that all solvability problems for linear#N#equation systems that separate fixed-point logic with counting from PTIME can#N#be reduced to solvability over commutative rings. Moreover, we prove closure#N#properties for classes of queries that reduce to solvability over rings, which#N#provides normal forms for logics extended with solvability operators. We#N#conclude by studying the extent to which fixed-point logic with counting can#N#express problems in linear algebra over finite commutative rings, generalising#N#known results on the logical definability of linear-algebraic problems over#N#finite fields.

Connected through hyperedge HE-1 (induced by source paper "approximations of isomorphism and logics with linear algebraic operators"):
  with members:
    - "a finite model theoretic view on propositional proof complexity"
    - "graph isomorphism in quasipolynomial time"
    - "rank logic is dead long live rank logic"
    - "pebble games and linear equations"
    - "pebble games with algebraic rules"

Connected through hyperedge HE-2 (induced by source paper "constraint satisfaction problem dichotomy for finite templates a proof via consistency checks"):
  with members:
    - "weaker consistency notions for all the csps of bounded width"
    - "space complexity of list h colouring a dichotomy"

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)