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 "leftmost outermost beta reduction is invariant indeed"):
  Abstract: Slot and van Emde Boas' weak invariance thesis states that reasonable machines can simulate each other within a polynomial overhead in time. Is λ-calculus a reasonable machine? Is there a way to measure the computational complexity of a λ-term? This paper presents the first complete positive answer to this long-standing problem. Moreover , our answer is completely machine-independent and based on a standard notion in the theory of λ-calculus: the length of a leftmost-outermost derivation to normal form is an invariant , i.e. reasonable, cost model. Such a theorem cannot be proved by directly relating λ-calculus with Turing machines or random access machines, because of the size-explosion problem: there are terms that in a linear number of steps produce an exponentially large output. The first step towards the solution is to shift to a notion of evaluation for which the length and the size of the output are linearly related. This is done by adopting the linear substitution calculus (LSC), a calculus of explicit substitutions modeled after linear logic proof nets and admitting a decomposition of leftmost-outermost derivations with the desired property. Thus, the LSC is invariant with respect to, say, random access machines. The second step is to show that the LSC is invariant with respect to the λ-calculus. The size explosion problem seems to imply that this is not possible: having the same notions of normal form, evaluation in the LSC is exponentially longer than in the λ-calculus. We solve such an impasse by introducing a new form of shared normal form and shared reduction , called useful. Useful evaluation produces a compact, shared representation of the normal form, by avoiding those steps that only unshare the output without contributing to β-redexes, i.e. the steps that cause the blow-up in size. The main technical contribution of the paper is indeed the definition of useful reductions and the thorough analysis of their properties.

Includes members:
  Member "maximal sharing in the lambda calculus with letrec":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "modeling terms by graphs with structure constraints two illustrations")
  Member "on constructor rewrite systems and the lambda calculus":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "on probabilistic term rewriting")
  Member "execution time of lambda terms via denotational semantics and intersection types":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "the bang calculus revisited")

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)