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 "nonlinear craig interpolant generation"):
  Abstract: Interpolation-based techniques have become popularized in recent years because of their inherently modular and local reasoning, which can scale up existing formal verification techniques like theorem proving, model-checking, abstraction interpretation, and so on, while the scalability is the bottleneck of these techniques. Craig interpolant generation plays a central role in interpolation-based techniques, and therefore has drawn increasing attentions. In the literature, there are various works done on how to automatically synthesize interpolants for decidable fragments of first-order logic, linear arithmetic, array logic, equality logic with uninterpreted functions (EUF), etc., and their combinations. But Craig interpolant generation for non-linear theory and its combination with the aforementioned theories are still in infancy, although some attempts have been done. In this paper, we first prove that a polynomial interpolant of the form $h(\mathbf{x})>0$ exists for two mutually contradictory polynomial formulas $\phi(\mathbf{x},\mathbf{y})$ and $\psi(\mathbf{x},\mathbf{z})$, with the form $f_1\ge0\wedge\cdots\wedge f_n\ge0$, where $f_i$ are polynomials in $\mathbf{x},\mathbf{y}$ or $\mathbf{x},\mathbf{z}$, and the quadratic module generated by $f_i$ is Archimedean. Then, we show that synthesizing such interpolant can be reduced to solving a semi-definite programming problem (${\rm SDP}$). In addition, we propose a verification approach to assure the validity of the synthesized interpolant and consequently avoid the unsoundness caused by numerical error in ${\rm SDP}$ solving. Finally, we discuss how to generalize our approach to general semi-algebraic formulas.

Includes members:
  Member "generating non linear interpolants by semidefinite programming":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "synthesizing basic semialgebraic invariants by semidefinite programming")
  Member "a hybrid approach for synthesizing optimal controllers of hybrid systems a case study of the oil pump industrial example":
    also connected through other hyperedges:
      (none)
  Member "interpolation in local theory extensions":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "nil learning nonlinear interpolants")

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.FL(Formal Languages and Automata Theory)