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 "open induction in a bounded arithmetic for tc0"):
  Abstract: The elementary arithmetic operations $${+,\cdot,\le}$$ + , · , ≤ on integers are well-known to be computable in the weak complexity class TC0, and it is a basic question what properties of these operations can be proved using only TC0-computable objects, i.e., in a theory of bounded arithmetic corresponding to TC0. We will show that the theory VTC 0 extended with an axiom postulating the totality of iterated multiplication (which is computable in TC0) proves induction for quantifier-free formulas in the language $${\langle{+,\cdot,\le}\rangle}$$ ? + , · , ≤ ? (IOpen), and more generally, minimization for $${\Sigma_{0}^{b}}$$ Σ 0 b formulas in the language of Buss's S 2.

Includes members:
  Member "root finding with threshold circuits":
    also connected through other hyperedges:
      (none)
  Member "theories for tc0 and other small complexity classes":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "relativizing small complexity classes and their theories")

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)