human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "coupling proofs are probabilistic product programs"
  Abstract: Couplings are a powerful mathematical tool for reasoning about pairs of probabilistic processes. Recent developments in formal verification identify a close connection between couplings and pRHL, a relational program logic motivated by applications to provable security, enabling formal construction of couplings from the probability theory literature. However, existing work using pRHL merely shows existence of a coupling and does not give a way to prove quantitative properties about the coupling, needed to reason about mixing and convergence of probabilistic processes. Furthermore, pRHL is inherently incomplete, and is not able to capture some advanced forms of couplings such as shift couplings. We address both problems as follows.     First, we define an extension of pRHL, called x-pRHL, which explicitly constructs the coupling in a pRHL derivation in the form of a probabilistic product program that simulates two correlated runs of the original program. Existing verification tools for probabilistic programs can then be directly applied to the probabilistic product to prove quantitative properties of the coupling. Second, we equip x-pRHL with a new rule for while loops, where reasoning can freely mix synchronized and unsynchronized loop iterations. Our proof rule can capture examples of shift couplings, and the logic is relatively complete for deterministic programs.     We show soundness of x-PRHL and use it to analyze two classes of examples. First, we verify rapid mixing using different tools from coupling: standard coupling, shift coupling, and path coupling, a compositional principle for combining local couplings into a global coupling. Second, we verify (approximate) equivalence between a source and an optimized program for several instances of loop optimizations from the literature.

Connected through hyperedge HE-1 (induced by source paper "proving expected sensitivity of probabilistic programs with randomized variable dependent termination time"):
  with members:
    - "kantorovich continuity of probabilistic programs"
    - "new approaches for almost sure termination of probabilistic programs"
    - "computational approaches for stochastic shortest path on succinct mdps"
    - "bounded expectations resource analysis for probabilistic programs"
    - "proving expected sensitivity of probabilistic programs"
    - "finding polynomial loop invariants for probabilistic programs"
    - "a new proof rule for almost sure termination"
    - "a semantic account of metric preservation"

Connected through hyperedge HE-2 (induced by source paper "proving expected sensitivity of probabilistic programs with randomized execution time"):
  with members:
    - "kantorovich continuity of probabilistic programs"
    - "computational approaches for stochastic shortest path on succinct mdps"
    - "bounded expectations resource analysis for probabilistic programs"
    - "proving expected sensitivity of probabilistic programs"
    - "a semantic account of metric preservation"
    - "termination analysis of probabilistic programs through positivstellensatz s"
    - "weakest precondition reasoning for expected run times of probabilistic programs"
    - "train faster generalize better stability of stochastic gradient descent"

Connected through hyperedge HE-3 (induced by source paper "the next 700 relational program logics"):
  with members:
    - "synthetic topology in homotopy type theory for probabilistic programming"
    - "formal verification of higher order probabilistic programs reasoning about approximation convergence bayesian inference and optimization"
    - "journey beyond full abstraction exploring robust property preservation for secure compilation"
    - "proof relevant logical relations for name generation"
    - "relational cost analysis for functional imperative programs"
    - "a relational logic for higher order programs"
    - "relational reasoning via probabilistic coupling"
    - "abstract effects and proof relevant logical relations"

Connected through hyperedge HE-4 (induced by source paper "relational reasoning for markov chains in a probabilistic guarded lambda calculus"):
  with members:
    - "proving uniformity and independence by self composition and coupling"
    - "the guarded lambda calculus programming and reasoning with guarded recursion for coinductive types"
    - "a relational logic for higher order programs"
    - "guarded dependent type theory with coinductive types"
    - "differentially private bayesian programming"
    - "relational reasoning via probabilistic coupling"
    - "a lambda calculus foundation for universal probabilistic programming"
    - "higher order approximate relational refinement types for mechanism design and differential privacy"

Connected through hyperedge HE-5 (induced by source paper "a separation logic for concurrent randomized programs"):
  with members:
    - "relational reasoning for markov chains in a probabilistic guarded lambda calculus"
    - "quantitative separation logic"
    - "proving uniformity and independence by self composition and coupling"
    - "a higher order logic for concurrent termination preserving refinement"
    - "a program logic for union bounds"
    - "weakest precondition reasoning for expected run times of probabilistic programs"
    - "relational reasoning via probabilistic coupling"
    - "step indexed logical relations for probability"

Connected through hyperedge HE-6 (induced by source paper "constraint based synthesis of coupling proofs"):
  with members:
    - "an assertion based program logic for probabilistic programs"
    - "synthesizing coupling proofs of differential privacy"
    - "proving expected sensitivity of probabilistic programs"
    - "proving uniformity and independence by self composition and coupling"
    - "probabilistic couplings for probabilistic reasoning"
    - "advanced probabilistic couplings for differential privacy"
    - "termination analysis of probabilistic programs through positivstellensatz s"
    - "proving differential privacy via probabilistic couplings"

Connected through hyperedge HE-7 (induced by source paper "proving expected sensitivity of probabilistic programs"):
  with members:
    - "a semantic account of metric preservation"
    - "developing bug free machine learning systems with formal mathematics"
    - "reluplex an efficient smt solver for verifying deep neural networks"
    - "liftings for differential privacy"
    - "probabilistic couplings for probabilistic reasoning"
    - "computer aided verification for mechanism design"
    - "advanced probabilistic couplings for differential privacy"
    - "without replacement sampling for stochastic gradient methods convergence results and application to distributed optimization"

Connected through hyperedge HE-8 (induced by source paper "synthesizing coupling proofs of differential privacy"):
  with members:
    - "proving uniformity and independence by self composition and coupling"
    - "a semantic account of metric preservation"
    - "liftings for differential privacy"
    - "lightdp towards automating differential privacy proofs"
    - "probabilistic couplings for probabilistic reasoning"
    - "advanced probabilistic couplings for differential privacy"
    - "understanding the sparse vector technique for differential privacy"
    - "approximate relational hoare logic for continuous random samplings"

Question: Please tell me which class the center node 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)