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 "optimal satisfiability checking for arithmetic mu calculi"):
  Abstract: The coalgebraic $\mu$-calculus provides a generic semantic framework for fixpoint logics with branching types beyond the standard relational setup, e.g. probabilistic, weighted, or game-based. Previous work on the coalgebraic $\mu$-calculus includes an exponential time upper bound on satisfiability checking, which however requires a well-behaved set of tableau rules for the next-step modalities. Such rules are not available in all cases of interest, in particular ones involving either integer weights as in the graded $\mu$-calculus, or real-valued weights in combination with non-linear arithmetic. In the present paper, we prove the same upper complexity bound under more general assumptions, specifically regarding the complexity of the (much simpler) satisfiability problem for the underlying so-called one-step logic, roughly described as the nesting-free next-step fragment of the logic. We also present a generic global caching algorithm that is suitable for practical use and supports on-the-fly satisfiability checking. Example applications include new exponential-time upper bounds for satisfiability checking in an extension of the graded $\mu$-calculus with Presburger arithmetic, as well as an extension of the (two-valued) probabilistic $\mu$-calculus with polynomial inequalities. As a side result, we moreover obtain a new upper bound $\mathcal{O}(((nk)!)^2)$ on minimum model size for satisfiable formulas for all coalgebraic $\mu$-calculi, where $n$ is the size of the formula and $k$ its alternation depth.

Includes members:
  Member "permutation games for the weakly aconjunctive mu calculus":
    also connected through other hyperedges:
      (none)
  Member "satisfiability games for branching time logics":
    also connected through other hyperedges:
      (none)
  Member "unifying buchi complementation constructions":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "simulations in rank based b uchi automata complementation technical report")
  Member "exptime tableaux for the coalgebraic mu calculus":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "np reasoning in the monotone mu calculus")
  Member "strong completeness of coalgebraic modal logics":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "completeness via canonicity in coalgebraic logics")
  Member "pspace bounds for rank 1 modal logics":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "categorical liveness checking by corecursive algebras")
  Member "decisive markov chains":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "decisiveness of stochastic systems and its application to hybrid models")

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)