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 "polynomial probabilistic invariants and the optional stopping theorem"):
  Abstract: In this paper we present methods for the synthesis of polynomial invariants for probabilistic transition systems. Our approach is based on martingale theory. We construct invariants in the form of polynomials over program variables, which give rise to martingales. These polynomials are program invariants in the sense that their expected value upon termination is the same as their value at the start of the computation. In order to guarantee this we apply the Optional Stopping Theorem. Concretely, we present two approaches. The first is restricted to linear systems. In this case under positive almost sure termination there is a reduction to finding linear invariants for deterministic transition systems. Secondly, by exploiting geometric persistence properties we construct martingale invariants for general polynomial transition system. We have implemented this approach and it works on our examples.

Includes members:
  Member "polynomial invariant generation for non deterministic recursive programs":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "automatic generation of moment based invariants for prob solvable loops")
  Member "compositional analysis for almost sure termination of probabilistic programs":
    also connected through other hyperedges:
      (none)
  Member "aiming low is harder inductive proof rules for lower bounds on weakest preexpectations in probabilistic program verification":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "tail bound analysis for probabilistic programs via central moments")
  Member "tail probabilities for randomized program runtimes via martingales for higher moments":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "automatic generation of moment based invariants for prob solvable loops")
  Member "finding polynomial loop invariants for probabilistic programs":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "proving expected sensitivity of probabilistic programs with randomized variable dependent termination time")
  Member "weakest precondition reasoning for expected run times of probabilistic programs":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "exponential automatic amortized resource analysis")
  Member "synthesizing probabilistic invariants via doob s decomposition":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "aiming low is harder inductive proof rules for lower bounds on weakest preexpectations in probabilistic program verification")
  Member "counterexample guided polynomial loop invariant generation by lagrange interpolation":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "aiming low is harder inductive proof rules for lower bounds on weakest preexpectations in probabilistic program verification")

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)