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 "quantified constraints and containment problems"):
  Abstract: The quantified constraint satisfaction problem $\mathrm{QCSP}(\mathcal{A})$#N#is the problem to decide whether a positive Horn sentence, involving nothing#N#more than the two quantifiers and conjunction, is true on some fixed structure#N#$\mathcal{A}$. We study two containment problems related to the QCSP. Firstly,#N#we give a combinatorial condition on finite structures $\mathcal{A}$ and#N#$\mathcal{B}$ that is necessary and sufficient to render#N#$\mathrm{QCSP}(\mathcal{A}) \subseteq \mathrm{QCSP}(\mathcal{B})$. We prove#N#that $\mathrm{QCSP}(\mathcal{A}) \subseteq \mathrm{QCSP}(\mathcal{B})$, that is#N#all sentences of positive Horn logic true on $\mathcal{A}$ are true on#N#$\mathcal{B}$, iff there is a surjective homomorphism from#N#$\mathcal{A}^{|A|^{|B|}}$ to $\mathcal{B}$. This can be seen as improving an#N#old result of Keisler that shows the former equivalent to there being a#N#surjective homomorphism from $\mathcal{A}^\omega$ to $\mathcal{B}$. We note#N#that this condition is already necessary to guarantee containment of the#N#$\Pi_2$ restriction of the QCSP, that is $\Pi_2$-$\mathrm{CSP}(\mathcal{A})#N#\subseteq \Pi_2$-$\mathrm{CSP}(\mathcal{B})$. The exponent's bound of#N#${|A|^{|B|}}$ places the decision procedure for the model containment problem#N#in non-deterministic double-exponential time complexity. We further show the#N#exponent's bound $|A|^{|B|}$ to be close to tight by giving a sequence of#N#structures $\mathcal{A}$ together with a fixed $\mathcal{B}$, $|B|=2$, such#N#that there is a surjective homomorphism from $\mathcal{A}^r$ to $\mathcal{B}$#N#only when $r \geq |A|$. Secondly, we prove that the entailment problem for#N#positive Horn fragment of first-order logic is decidable. That is, given two#N#sentences $\varphi$ and $\psi$ of positive Horn, we give an algorithm that#N#determines whether $\varphi \rightarrow \psi$ is true in all structures#N#(models). Our result is in some sense tight, since we show that the entailment#N#problem for positive first-order logic (i.e. positive Horn plus disjunction) is#N#undecidable. In the final part of the paper we ponder a notion of Q-core that#N#is some canonical representative among the class of templates that engender the#N#same QCSP. Although the Q-core is not as well-behaved as its better known#N#cousin the core, we demonstrate that it is still a useful notion in the realm#N#of QCSP complexity classifications.

Includes members:
  Member "containment equivalence and coreness from csp to qcsp and beyond":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "from complexity to algebra and back digraph classes collapsibility and the pgp")
  Member "the complexity of quantified constraint satisfaction collapsibility sink algebras and the three element case":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "qcsp monsters and the demise of the chen conjecture")
  Member "semantical characterizations and complexity of equivalences in answer set programming":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "query inseparability for alc ontologies")

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.LO(Logic in Computer Science)