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 "lower bounds on the redundancy in computations from random oracles via betting strategies with restricted wagers"):
  Abstract: The Ku\v{c}era-G\'{a}cs theorem is a landmark result in algorithmic randomness asserting that every real is computable from a Martin-L\"{o}f random real. If the computation of the first $n$ bits of a sequence requires $n+h(n)$ bits of the random oracle, then $h$ is the redundancy of the computation. Ku\v{c}era implicitly achieved redundancy $n\log n$ while G\'{a}cs used a more elaborate coding procedure which achieves redundancy $\sqrt{n}\log n$. A similar upper bound is implicit in the later proof by Merkle and Mihailovi\'{c}. In this paper we obtain strict optimal lower bounds on the redundancy in computations from Martin-L\"{o}f random oracles. We show that any nondecreasing computable function $g$ such that $\sum_n 2^{-g(n)}=\infty$ is not a general upper bound on the redundancy in computations from Martin-L\"{o}f random oracles. In fact, there exists a real $X$ such that the redundancy $g$ of any computation of $X$ from a Martin-L\"{o}f random oracle satisfies $\sum_n 2^{-g(n)}<\infty$. Moreover, the class of such reals is comeager and includes a $\Delta^0_2$ real as well as all weakly 2-generic reals. This excludes many slow growing functions such as $\log n$ from bounding the redundancy in computations from random oracles for a large class of reals. On the other hand it was recently shown that if $\sum_n 2^{-g(n)}<\infty$ then $g$ is a general upper bound for the redundancy in computations of any real from some Martin-L\"{o}f random oracle. Our results are obtained as an application of a theory of effective betting strategies with restricted wagers which we develop.

Includes members:
  Member "optimal redundancy in computations from random oracles":
    also connected through other hyperedges:
      (none)
  Member "integer valued betting strategies and turing degrees":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "granularity of wagers in games and the im possibility of savings")
  Member "how to gamble against all odds":
    also connected through other hyperedges:
      (none)
  Member "how powerful are integer valued martingales":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "granularity of wagers in games and the im possibility of savings")
  Member "every sequence is decompressible from a random one":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "compression of data streams down to their information content")

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)