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 "monotone 3 sat 2 2 is np complete"):
  Abstract: We show that Monotone 3-Sat remains NP-complete if (i) each clause contains exactly three distinct variables, (ii) each clause is unique, i.e., there are no duplicates of the same clause, and (iii), amongst the clauses, each variable appears unnegated exactly twice and negated exactly twice. Darmann and Docker [6] recently showed that this variant of Monotone 3-Sat is either trivial or NP-complete. In the first part of the paper, we construct an unsatisfiable instance which answers one of their open questions (Challenge 1) and places the problem in the latter category. #R##N#Then, we adapt gadgets used in the construction to (1) sketch two reductions that establish NP-completeness in a more direct way, and (2), to show that $\forall\exists$ 3-SAT remains $\Pi_2^P$-complete for quantified Boolean formulas with the following properties: (a) each clause is monotone (i.e., no clause contains an unnegated and a negated variable) and contains exactly three distinct variables, (b) each universal variable appears exactly once unnegated and exactly once negated, (c) each existential variable appears exactly twice unnegated and exactly twice negated, and (d) the number of universal and existential variables is equal. Furthermore, we show that the variant where (b) is replaced with (b') each universal variable appears exactly twice unnegated and exactly twice negated, and where (a), (c) and (d) are unchanged, is $\Pi_2^P$-complete as well. Thereby, we improve upon two recent results by Docker et al. [8] that establish $\Pi_2^P$-completeness of these variants in the non-monotone setting. #R##N#We also discuss a special case of Monotone 3-Sat-(2,2) that corresponds to a variant of Not-All-Equal Sat, and we show that all such instances are satisfiable.

Includes members:
  Member "on simplified np complete variants of not all equal 3 sat and 3 sat":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "placing quantified variants of 3 sat and not all equal 3 sat in the polynomial hierarchy")
  Member "placing quantified variants of 3 sat and not all equal 3 sat in the polynomial hierarchy":
    also connected through other hyperedges:
      (none)
  Member "on a variant of monotone nae 3sat and the triangle free cut problem":
    also connected through other hyperedges:
      (none)

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.CC(Computational Complexity)