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 template generation using sum of squares programming"):
  Abstract: Template abstract domains allow to express more interesting properties than classical abstract domains. However, template generation is a challenging problem when one uses template abstract domains for program analysis. In this paper, we relate template generation with the program properties that we want to prove. We focus on one-loop programs with nested conditional branches. We formally define the notion of well-representative template basis with respect to such programs and a given property. The definition relies on the fact that template abstract domains produce inductive invariants. We show that these invariants can be obtained by solving certain systems of functional inequalities. Then, such systems can be strengthened using a hierarchy of sum-of-squares (SOS) problems when we consider programs written in polynomial arithmetic. Each step of the SOS hierarchy can possibly provide a solution which in turn yields an invariant together with a certificate that the desired property holds. The interest of this approach is illustrated on nontrivial program examples in polynomial arithmetic.

Includes members:
  Member "certification of bounds of non linear functions the templates method":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "formal proofs for nonlinear optimization")
  Member "coupling policy iteration with semi definite relaxation to compute accurate numerical invariants in static analysis":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "synthesizing invariants by solving solvable loops")
  Member "exact safety verification of hybrid systems using sums of squares representation":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "property based polynomial invariant generation using sums of squares optimization")

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)