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 "long run average behavior of vector addition systems with states"):
  Abstract: A vector addition system with states (VASS) consists of a finite set of states and counters. A configuration is a state and a value for each counter; a transition changes the state and each counter is incremented, decremented, or left unchanged. While qualitative properties such as state and configuration reachability have been studied for VASS, we consider the long-run average cost of infinite computations of VASS. The cost of a configuration is for each state, a linear combination of the counter values. In the special case of uniform cost functions, the linear combination is the same for all states. The (regular) long-run emptiness problem is, given a VASS, a cost function, and a threshold value, if there is a (lasso-shaped) computation such that the long-run average value of the cost function does not exceed the threshold. For uniform cost functions, we show that the regular long-run emptiness problem is (a)~decidable in polynomial time for integer-valued VASS, and (b)~decidable but nonelementarily hard for natural-valued VASS (i.e., nonnegative counters). For general cost functions, we show that the problem is (c)~NP-complete for integer-valued VASS, and (d)~undecidable for natural-valued VASS. Our most interesting result is for (c) integer-valued VASS with general cost functions, where we establish a connection between the regular long-run emptiness problem and quadratic Diophantine inequalities. The general (nonregular) long-run emptiness problem is equally hard as the regular problem in all cases except (c), where it remains open.

Includes members:
  Member "the reachability problem for petri nets is not elementary":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "reachability in fixed dimension vector addition systems with states")
  Member "nested weighted limit average automata of bounded width":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "bidirectional nested weighted automata")
  Member "average energy games":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "games where you can play optimally with finite memory")
  Member "long run average behaviour of probabilistic vector addition systems":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "qualitative analysis of vass induced mdps")
  Member "mixed integer quadratic programming is in np":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "deep hypernetwork based mimo detection")
  Member "reachability games on extended vector addition systems with states":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "energy mean payoff games")

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.FL(Formal Languages and Automata Theory)