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 "finding polynomial loop invariants for probabilistic programs"):
  Abstract: Quantitative loop invariants are an essential element in the verification of probabilistic programs. Recently, multivariate Lagrange interpolation has been applied to synthesizing polynomial invariants. In this paper, we propose an alternative approach. First, we fix a polynomial template as a candidate of a loop invariant. Using Stengle's Positivstellensatz and a transformation to a sum-of-squares problem, we find sufficient conditions on the coefficients. Then, we solve a semidefinite programming feasibility problem to synthesize the loop invariants. If the semidefinite program is unfeasible, we backtrack after increasing the degree of the template. Our approach is semi-complete in the sense that it will always lead us to a feasible solution if one exists and numerical errors are small. Experimental results show the efficiency of our approach.

Includes members:
  Member "termination analysis of probabilistic programs through positivstellensatz s":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "tail bound analysis for probabilistic programs via central moments")
  Member "synthesizing probabilistic invariants via doob s decomposition":
    also connected through other hyperedges:
      - Hyperedge HE-2 (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-3 (induced by source paper "aiming low is harder inductive proof rules for lower bounds on weakest preexpectations in probabilistic program verification")
  Member "on the hardness of almost sure termination":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "aiming low is harder inductive proof rules for lower bounds on weakest preexpectations in probabilistic program verification")
  Member "generating non linear interpolants by semidefinite programming":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "synthesizing basic semialgebraic invariants by semidefinite programming")
  Member "proving inequalities and solving global optimization problems via simplified cad projection":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "finding best possible constant for a polynomial inequality")

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)