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 "satisfying assignments of random boolean csp clusters and overlaps"):
  Abstract: The distribution of overlaps of solutions of a random CSP is an indicator of the overall geometry of its solution space. For random $k$-SAT, nonrigorous methods from Statistical Physics support the validity of the ``one step replica symmetry breaking'' approach. Some of these predictions were rigorously confirmed in \cite{cond-mat/0504070/prl} \cite{cond-mat/0506053}. There it is proved that the overlap distribution of random $k$-SAT, $k\geq 9$, has discontinuous support. Furthermore, Achlioptas and Ricci-Tersenghi proved that, for random $k$-SAT, $k\geq 8$. and constraint densities close enough to the phase transition there exists an exponential number of clusters of satisfying assignments; moreover, the distance between satisfying assignments in different clusters is linear. #R##N#We aim to understand the structural properties of random CSP that lead to solution clustering. To this end, we prove two results on the cluster structure of solutions for binary CSP under the random model from Molloy (STOC 2002) #R##N#1. For all constraint sets $S$ (described explicitly in Creignou and Daude (2004), Istrate (2005)) s.t. $SAT(S)$ has a sharp threshold and all $q\in (0,1]$, $q$-overlap-$SAT(S)$ has a sharp threshold (i.e. the first step of the approach in Mora et al. works in all nontrivial cases). 2. For any constraint density value $c<1$, the set of solutions of a random instance of 2-SAT form, w.h.p., a single cluster. Also, for and any $q\in (0,1]$ such an instance has w.h.p. two satisfying assignment of overlap $\sim q$. Thus, as expected from Statistical Physics predictions, the second step of the approach in Mora et al. fails for 2-SAT.

Includes members:
  Member "the connectivity of boolean satisfiability computational and structural dichotomies":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "dominating sets reconfiguration under token sliding")
  Member "on the solution space geometry of random constraint satisfaction problems":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "quantitative verification of neural networks and its security applications")
  Member "threshold values of random k sat from the cavity method":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "hierarchical decomposition mechanism by konig egervary layer subgraph with application on vertex cover")
  Member "survey propagation an algorithm for satisfiability":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "pdp a general neural framework for learning constraint satisfaction solvers")

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.DM(Discrete Mathematics)