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: "probabilistic couplings for probabilistic reasoning"
  Abstract: This thesis explores proofs by coupling from the perspective of formal verification. Long employed in probability theory and theoretical computer science, these proofs construct couplings between the output distributions of two probabilistic processes. Couplings can imply various guarantees comparing two runs of a probabilistic computation. We first show that proofs in the program logic pRHL describe couplings. We formalize couplings that establish various probabilistic properties, including distribution equivalence, convergence, and stochastic domination. Then we give a proofs-as-programs interpretation: a coupling proof encodes a probabilistic product program, whose properties imply relational properties of the original programs. We design the logic xpRHL to construct the product, with extensions to model shift coupling and path coupling. We then propose an approximate version of probabilistic coupling and a corresponding proof technique---proof by approximate coupling---inspired by the logic apRHL, a version of pRHL for building approximate liftings. Drawing on ideas from existing privacy proofs, we extend apRHL with novel proof rules for constructing new approximate couplings. We give an approximate coupling proof of privacy for the Sparse Vector mechanism, a well-known algorithm from the privacy literature whose privacy proof is notoriously subtle, and produce the first formalized proof of privacy for Sparse Vector in apRHL. Finally, we propose several more sophisticated constructions for approximate couplings: a principle for showing accuracy-dependent privacy, a generalization of the advanced composition theorem, and an optimal approximate coupling relating two subsets. We also show equivalences between our approximate couplings and other existing definitions. These ingredients support the first formalized proof of privacy for the Between Thresholds mechanism.

Connected through hyperedge HE-1 (induced by source paper "relational proofs for quantum programs"):
  with members:
    - "quantum relational hoare logic with expectations"
    - "quantitative robustness analysis of quantum programs"
    - "proving expected sensitivity of probabilistic programs"
    - "proving uniformity and independence by self composition and coupling"
    - "proving differential privacy via probabilistic couplings"
    - "relational reasoning via probabilistic coupling"
    - "toward automatic verification of quantum cryptographic protocols"
    - "verification of quantum programs"

Connected through hyperedge HE-2 (induced by source paper "fuzzi a three level logic for differential privacy"):
  with members:
    - "approximate span liftings compositional semantics for relaxations of differential privacy"
    - "ektelo a framework for defining differentially private computations"
    - "detecting violations of differential privacy"
    - "synthesizing coupling proofs of differential privacy"
    - "learning differentially private recurrent language models"
    - "towards practical differential privacy for sql queries"
    - "lightdp towards automating differential privacy proofs"
    - "psi ψ a private data sharing interface"

Connected through hyperedge HE-3 (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"
    - "coupling proofs are probabilistic product programs"
    - "advanced probabilistic couplings for differential privacy"
    - "termination analysis of probabilistic programs through positivstellensatz s"
    - "proving differential privacy via probabilistic couplings"

Connected through hyperedge HE-4 (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"
    - "coupling proofs are probabilistic product programs"
    - "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-5 (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"
    - "coupling proofs are probabilistic product programs"
    - "lightdp towards automating differential privacy proofs"
    - "advanced probabilistic couplings for differential privacy"
    - "understanding the sparse vector technique for differential privacy"
    - "approximate relational hoare logic for continuous random samplings"

Connected through hyperedge HE-6 (induced by source paper "a language for probabilistically oblivious computation"):
  with members:
    - "trace abstraction modulo probability"
    - "proving uniformity and independence by self composition and coupling"
    - "coupling proofs are probabilistic product programs"
    - "lightdp towards automating differential privacy proofs"
    - "higher order approximate relational refinement types for mechanism design and differential privacy"
    - "privacy preserving data oblivious geometric algorithms for geographic data"

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.LO(Logic in Computer Science)