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 "parameterised counting classes tail versus reductions"):
  Abstract: Stockhusen and Tantau (IPEC 2013) defined the operators paraW- and paraBeta- for parameterised space complexity classes by allowing bounded nondeterminism with multiple read and read-once access, respectively. Using these operators, they characterised the complexity for many parameterisations of natural problems on graphs. In this article, we study the counting versions of such operators and introduce variants based on tail-nondeterminism, paraW[1]- and paraBetaTail-, in the setting of parameterised logarithmic space. Initially, we examine closure properties of such classes under the central reductions as well as arithmetic operations. We prove that the closure of the class #paraBetaTail-L under parsimonious parameterised logspace reductions coincides with #paraBeta-L. We identify natural path counting problems in digraphs that are complete for the newly introduced classes #paraW-L and #paraBeta-L. We study the complexity of counting variants of model checking problems for specific classes of FO-formulas, and find complete versions for #paraBetaTail-L and #paraW[1]-L. Furthermore, we present a counting variant of a parameterised homomorphism problem, where the input structure is a coloured path, which is complete for the class #paraBeta-L. Afterwards, we show that the complexity of a parameterised variant of the determinant function is #paraBetaTail-L-hard and can be written as the difference of two functions in #paraBetaTail-L for 0/1 matrices. Also, we characterise the new complexity classes in terms of branching programs.

Includes members:
  Member "fast parallel fixed parameter algorithms via color coding":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "dynamic complexity meets parameterised algorithms")
  Member "block interpolation a framework for tight exponential time counting complexity":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "the exact complexity of the tutte polynomial")
  Member "parameterized analogues of probabilistic computation":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "probabilistic parameterized polynomial time")
  Member "completeness results for parameterized space classes":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "nominal automata with name binding")

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)