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 "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.

Includes members:
  Member "proof relevant logical relations for name generation":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "the next 700 relational program logics")
  Member "a program logic for union bounds":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "unifying graded and parameterised monads")
  Member "approximate relational hoare logic for continuous random samplings":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "duet an expressive higher order language and linear type system for statically enforcing differential privacy")
  Member "proving differential privacy via probabilistic couplings":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "guidelines for implementing and auditing differentially private systems")
  Member "relational reasoning via probabilistic coupling":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "relational proofs for quantum programs")
  Member "higher order approximate relational refinement types for mechanism design and differential privacy":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "guidelines for implementing and auditing differentially private systems")
  Member "step indexed logical relations for probability":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "on the versatility of open logical relations continuity automatic differentiation and a containment theorem")
  Member "proving differential privacy in hoare logic":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "guidelines for implementing and auditing differentially private systems")

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)