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 "ackermannian and primitive recursive bounds with dickson s lemma"):
  Abstract: Dickson's Lemma is a simple yet powerful tool widely used in decidability proofs, especially when dealing with counters or related data structures in algorithmics, verification and model-checking, constraint solving, logic, etc. While Dickson's Lemma is well-known, most computer scientists are not aware of the complexity upper bounds that are entailed by its use. This is mainly because, on this issue, the existing literature is not very accessible. We propose a new analysis of the length of bad sequences over $(\mathbb{N}^k,\leq)$, improving on earlier results and providing upper bounds that are essentially tight. This analysis is complemented by a ``user guide'' explaining through practical examples how to easily derive complexity upper bounds from Dickson's Lemma.

Includes members:
  Member "multiply recursive upper bounds with higman s lemma":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "the ideal approach to computing closed subsets in well quasi orderings")
  Member "on pebble automata for data languages with decidable emptiness problem":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "complexity hierarchies beyond elementary")
  Member "ltl with the freeze quantifier and register automata":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "on computability of data word functions defined by transducers")

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)