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 "on numerical error propagation with sensitivity"):
  Abstract: An emerging area of research is to automatically compute reasonably precise upper bounds on numerical errors including roundoffs. Previous approaches for this task are limited in their precision and scalability, especially in the presence of branches and loops. We argue that one reason for these limitations is the focus of past approaches on approximating errors of individual reachable states. We propose instead a more relational and modular approach to analysis that characterizes analytically the input/output behavior of code fragments and reuses this characterization to reason about larger code fragments. We use the derivatives of the functions corresponding to program paths to capture a program's sensitivity to input changes. To apply this approach for finite-precision code, we decouple the computation of newly introduced roundoff errors from the amplification of existing errors. This enables us to precisely and efficiently account for propagation of errors through long-running computation. Using this approach we implemented an analysis for programs containing nonlinear computation, conditionals, and loops. In the presence of loops our approach can find closed-form symbolic invariants capturing upper bounds on numerical errors, even when the error grows with the number of iterations. We evaluate our system on a number of benchmarks from embedded systems and scientific computation, showing substantial improvements in precision and scalability over the state of the art. Limitations of state of the art tools. Existing state-of-the-art sound and automated error estimation techniques rely on stepwise application of affine arithmetic (AA) (14), which, due to its linear nature, inevitably introduce over-approximations when applied to nonlinear functions. Fluctuat (19) is an abstract interpretation based tool which uses affine arithmetic both for the range and the error computation, but adds constraints on the noise terms to improve the ranges computed by AA (18). Rosa (13) improves ranges with an SMT- backed procedure, but uses for the error computation essentially the same technique as Fluctuat. Affine arithmetic tracks a computation step by step, and thus fails to capture the overall effect of a function on uncertainties. When it comes to loops, roundoff errors may accumulate without a constant upper bound. Fluctuat is forced to unroll loops or apply widening, often returning a trivial upper bound of1 in such cases. Rosa can only handle recursive functions with given inductive specifications with constant absolute error bounds. Such specifications do not exist in general and furthermore, Rosa does not compute these specifications automatically. Finally, both Fluctuat and Rosa include a procedure to soundly estimate discontinuity errors, but the approaches work well only for linear or unary functions, severely limiting the analysis of numerical code containing branches. Separation of Errors We propose a new error computation based on separating the propagation of existing errors from the roundoff or truncation errors committed during the computation. This sep- aration allows us to distinguish the implementation aspects from the mathematical properties of the underlying function and handle them individually with appropriate techniques. In particular, this separation allows us to directly use the properties of the real-valued functions underlying the finite-precision implementation. Such a separation of errors applies fairly generally: it enabled us to 1) im- prove computed error bounds on straight-line nonlinear code, 2) characterize errors in loops as functions of the number of itera- tions, and 3) scale discontinuity error computations to multivariate functions. Propagation and Sensitivity Using the separation of errors, our new propagation procedure improves the computed error bounds compared to affine arithmetic. Our approach considers an entire arithmetic expression at a time, computing an approximation of the global effect of the function on the input errors, in contrast to the local linear approximation of affine arithmetic. Additionally, our procedure is backed by a nonlinear SMT-solver, which allows us to capture nonlinear correlations precisely. This can then be used for computing more precise bounds on the propagation error. Moreover, it provides information about the sensitivity of the function with respect to the errors, which is useful for understanding the behavior of the function and for modular inter-procedural analysis. We primarily use an approximation that is a linear expression in the input errors, based on the Jacobian of the (entire) function. We also develop a higher-order extension which can, for the first time,

Includes members:
  Member "robustness analysis of finite precision implementations":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "automatic generation and verification of test stable floating point code")
  Member "a non local method for robustness analysis of floating point programs":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "towards a compiler for reals")
  Member "a logical product approach to zonotope intersection":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "automatic generation and verification of test stable floating point code")
  Member "relational abstract domains for the detection of floating point run time errors":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "exploiting verified neural networks via floating point numerical error")
  Member "a static analyzer for large safety critical software":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "automatically proving microkernels free from privilege escalation from their executable")

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.PL(Programming Languages)