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 "approximations of isomorphism and logics with linear algebraic operators"):
  Abstract: Invertible map equivalences are approximations of graph isomorphism that refine the well-known Weisfeiler-Leman method. They are parametrised by a number k and a set Q of primes. The intuition is that two graphs G and H which are equivalent with respect to k-Q-IM-equivalence cannot be distinguished by a refinement of k-tuples given by linear operators acting on vector spaces over fields of characteristic p, for any p in Q. These equivalences first appeared in the study of rank logic, but in fact they can be used to delimit the expressive power of any extension of fixed-point logic with linear-algebraic operators. We define an infinitary logic with k variables and all linear-algebraic operators over finite vector spaces of characteristic p in Q and show that the k-Q-IM-equivalence is the natural notion of elementary equivalence for this logic. #R##N#By means of a new and much deeper algebraic analysis of a generalized variant, for any prime p, of the CFI-structures due to Cai, Furer, and Immerman, we prove that, as long as Q is not the set of all primes, there is no k such that k-Q-IM-equivalence is the same as isomorphism. It follows that there are polynomial-time properties of graphs which are not definable in the infinitary logic with all Q-linear-algebraic operators and finitely many variables, which implies that no extension of fixed-point logic with linear-algebraic operators can capture PTIME, unless it includes such operators for all prime characteristics. Our analysis requires substantial algebraic machinery, including a homogeneity property of CFI-structures and Maschke's Theorem, an important result from the representation theory of finite groups.

Includes members:
  Member "a finite model theoretic view on propositional proof complexity":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "counting bounded tree depth homomorphisms")
  Member "graph isomorphism in quasipolynomial time":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "hypergraph isomorphism for groups with restricted composition factors")
  Member "rank logic is dead long live rank logic":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "on the expressive power of linear algebra on graphs")
  Member "definability of linear equation systems over groups and rings":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "constraint satisfaction problem dichotomy for finite templates a proof via consistency checks")
  Member "pebble games and linear equations":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "a survey on the expressive power of graph neural networks")
  Member "pebble games with algebraic rules":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "on the expressive power of linear algebra on graphs")

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)