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: "short proofs for the determinant identities"
  Abstract: We study arithmetic proof systems P_c(F) and P_f(F) operating with arithmetic circuits and arithmetic formulas, respectively, that prove polynomial identities over a field F. We establish a series of structural theorems about these proof systems, the main one stating that P_c(F) proofs can be balanced: if a polynomial identity of syntactic degree d and depth k has a P_c(F) proof of size s, then it also has a P_c(F) proof of size poly(s,d) and depth O(k+\log^2 d + \log d\cd \log s). As a corollary, we obtain a quasipolynomial simulation of P_c(F) by P_f(F), for identities of a polynomial syntactic degree. #R##N#Using these results we obtain the following: consider the identities det(XY) = det(X)det(Y) and det(Z)= z_{11}... z_{nn}, where X,Y and Z are nxn square matrices and Z is a triangular matrix with z_{11},..., z_{nn} on the diagonal (and det is the determinant polynomial). Then we can construct a polynomial-size arithmetic circuit det such that the above identities have P_c(F) proofs of polynomial-size and O(\log^2 n) depth. Moreover, there exists an arithmetic formula det of size n^{O(\log n)} such that the above identities have P_f(F) proofs of size n^{O(\log n)}. #R##N#This yields a solution to a basic open problem in propositional proof complexity, namely, whether there are polynomial-size NC^2-Frege proofs for the determinant identities and the hard matrix identities, as considered, e.g., in Soltys and Cook (2004) (cf., Beame and Pitassi (1998)). We show that matrix identities like AB=I {\to} BA=I (for matrices over the two element field) as well as basic properties of the determinant have polynomial-size NC^2-Frege proofs, and quasipolynomial-size Frege proofs.

Connected through hyperedge HE-1 (induced by source paper "on algebraic branching programs of small width"):
  with members:
    - "the complexity of factors of multivariate polynomials"
    - "succinct hitting sets and barriers to proving algebraic circuits lower bounds"
    - "functional lower bounds for arithmetic circuits and connections to boolean circuit complexity"
    - "no occurrence obstructions in geometric complexity theory"
    - "a 2n 2 log n 1 lower bound for the border rank of matrix multiplication"
    - "boundaries of vp and vnp"
    - "unifying known lower bounds via geometric complexity theory"
    - "a lower bound for the determinantal complexity of a hypersurface"

Connected through hyperedge HE-2 (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-3 (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"
    - "algebraic proofs over noncommutative formulas"
    - "resolution over linear equations and multilinear proofs"

Connected through hyperedge HE-4 (induced by source paper "generating matrix identities and proof complexity"):
  with members:
    - "circuit complexity proof complexity and polynomial identity testing"

Connected through hyperedge HE-5 (induced by source paper "short propositional refutations for dense random 3cnf formulas"):
  with members:
    - "theories for tc0 and other small complexity classes"

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)