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 power of the weak"):
  Abstract: A landmark result in the study of logics for formal verification is Janin & Walukiewicz's theorem, stating that the modal $\mu$-calculus ($\mu\mathrm{ML}$) is equivalent modulo bisimilarity to standard monadic second-order logic (here abbreviated as $\mathrm{smso}$), over the class of labelled transition systems (LTSs for short). Our work proves two results of the same kind, one for the alternation-free fragment of $\mu\mathrm{ML}$ ($\mu_D\mathrm{ML}$) and one for weak $\mathrm{mso}$ ($\mathrm{wmso}$). Whereas it was known that $\mu_D\mathrm{ML}$ and $\mathrm{wmso}$ are equivalent modulo bisimilarity on binary trees, our analysis shows that the picture radically changes once we reason over arbitrary LTSs. The first theorem that we prove is that, over LTSs, $\mu_D\mathrm{ML}$ is equivalent modulo bisimilarity to noetherian $\mathrm{mso}$ ($\mathrm{nmso}$), a newly introduced variant of $\mathrm{smso}$ where second-order quantification ranges over "well-founded" subsets only. Our second theorem starts from $\mathrm{wmso}$, and proves it equivalent modulo bisimilarity to a fragment of $\mu_D\mathrm{ML}$ defined by a notion of continuity. Analogously to Janin & Walukiewicz's result, our proofs are automata-theoretic in nature: as another contribution, we introduce classes of parity automata characterising the expressiveness of $\mathrm{wmso}$ and $\mathrm{nmso}$ (on tree models) and of $\mu_C\mathrm{ML}$ and $\mu_D\mathrm{ML}$ (for all transition systems).

Includes members:
  Member "model theory of monadic predicate logic with the infinity quantifier":
    also connected through other hyperedges:
      (none)
  Member "weak mso automata and expressiveness modulo bisimilarity":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "bisimulation invariant monadic second order logic in the finite")

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)