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 "the isomorphism problem for omega automatic trees"):
  Abstract: The main result of this paper is that the isomorphism for omega-automatic trees of finite height is at least has hard as second-order arithmetic and therefore not analytical. This strengthens a recent result by Hjorth, Khoussainov, Montalban, and Nies showing that the isomorphism problem for omega-automatic structures is not $\Sigma^1_2$. Moreover, assuming the continuum hypothesis CH, we can show that the isomorphism problem for omega-automatic trees of finite height is recursively equivalent with second-order arithmetic. On the way to our main results, we show lower and upper bounds for the isomorphism problem for omega-automatic trees of every finite height: (i) It is decidable ($\Pi^0_1$-complete, resp,) for height 1 (2, resp.), (ii) $\Pi^1_1$-hard and in $\Pi^1_2$ for height 3, and (iii) $\Pi^1_{n-3}$- and $\Sigma^1_{n-3}$-hard and in $\Pi^1_{2n-4}$ (assuming CH) for all n > 3. All proofs are elementary and do not rely on theorems from set theory.

Includes members:
  Member "the isomorphism problem on classes of automatic structures":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "the isomorphism problem for tree automatic ordinals with addition")
  Member "highly undecidable problems for infinite computations":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "infinite games specified by 2 tape automata")
  Member "automatic structures richness and limitations":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "automatic supermartingales acting on sequences")

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)