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: "algebraic proofs over noncommutative formulas"
  Abstract: We study possible formulations of algebraic propositional proof systems operating with noncommutative formulas. We observe that a simple formulation gives rise to systems at least as strong as Frege---yielding a semantic way to define a Cook-Reckhow (i.e., polynomially verifiable) algebraic analog of Frege proofs, different from that given in [BIKPRS96,GH03]. We then turn to an apparently weaker system, namely, polynomial calculus (PC) where polynomials are written as ordered formulas (PC over ordered formulas, for short): an ordered polynomial is a noncommutative polynomial in which the order of products in every monomial respects a fixed linear order on variables; an algebraic formula is ordered if the polynomial computed by each of its subformulas is ordered. We show that PC over ordered formulas is strictly stronger than resolution, polynomial calculus and polynomial calculus with resolution (PCR) and admits polynomial-size refutations for the pigeonhole principle and the Tseitin's formulas. We conclude by proposing an approach for establishing lower bounds on PC over ordered formulas proofs, and related systems, based on properties of lower bounds on noncommutative formulas. #R##N#The motivation behind this work is developing techniques incorporating rank arguments (similar to those used in algebraic circuit complexity) for establishing lower bounds on propositional proofs.

Connected through hyperedge HE-1 (induced by source paper "proof complexity lower bounds from algebraic circuit complexity"):
  with members:
    - "functional lower bounds for arithmetic circuits and connections to boolean circuit complexity"
    - "an exponential lower bound for homogeneous depth 5 circuits over finite fields"
    - "identity testing and lower bounds for read k oblivious algebraic branching programs"
    - "circuit complexity proof complexity and polynomial identity testing"
    - "subexponential size hitting sets for bounded depth multilinear formulas"
    - "hitting sets for roabp and sum of set multilinear circuits"
    - "deterministic identity testing for sum of read once oblivious arithmetic branching programs"
    - "explicit noether normalization for simultaneous conjugation via polynomial identity testing"

Connected through hyperedge HE-2 (induced by source paper "algebraic proof complexity progress frontiers and challenges"):
  with members:
    - "functional lower bounds for arithmetic circuits and connections to boolean circuit complexity"
    - "proof complexity lower bounds from algebraic circuit complexity"
    - "a deterministic polynomial time algorithm for non commutative rational identity testing"
    - "generating matrix identities and proof complexity"
    - "circuit complexity proof complexity and polynomial identity testing"
    - "short proofs for the determinant identities"
    - "resolution over linear equations and multilinear proofs"

Connected through hyperedge HE-3 (induced by source paper "characterizing propositional proofs as non commutative formulas"):
  with members:
    - "generating matrix identities and proof complexity"
    - "circuit complexity proof complexity and polynomial identity testing"

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.CC(Computational Complexity)