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 "noncommutative valiant s classes structure and complete problems"):
  Abstract: In this paper we explore the noncommutative analogues, $\mathrm{VP}_{nc}$ and $\mathrm{VNP}_{nc}$, of Valiant's algebraic complexity classes and show some striking connections to classical formal language theory. Our main results are the following: (1) We show that Dyck polynomials (defined from the Dyck languages of formal language theory) are complete for the class $\mathrm{VP}_{nc}$ under $\le_{abp}$ reductions. Likewise, it turns out that $\mathrm{PAL}$ (Palindrome polynomials defined from palindromes) are complete for the class $\mathrm{VSKEW}_{nc}$ (defined by polynomial-size skew circuits) under $\le_{abp}$ reductions. The proof of these results is by suitably adapting the classical Chomsky-Sch\"{u}tzenberger theorem showing that Dyck languages are the hardest CFLs. (2) Next, we consider the class $\mathrm{VNP}_{nc}$. It is known~\cite{HWY10a} that, assuming the sum-of-squares conjecture, the noncommutative polynomial $\sum_{w\in\{x_0,x_1\}^n}ww$ requires exponential size circuits. We unconditionally show that $\sum_{w\in\{x_0,x_1\}^n}ww$ is not $\mathrm{VNP}_{nc}$-complete under the projection reducibility. As a consequence, assuming the sum-of-squares conjecture, we exhibit a strictly infinite hierarchy of p-families under projections inside $\mathrm{VNP}_{nc}$ (analogous to Ladner's theorem~\cite{Ladner75}). In the final section we discuss some new $\mathrm{VNP}_{nc}$-complete problems under $\le_{abp}$-reductions. (3) Inside $\mathrm{VP}_{nc}$ too we show there is a strict hierarchy of p-families (based on the nesting depth of Dyck polynomials) under the $\le_{abp}$ reducibility.

Includes members:
  Member "the complexity of the fermionant and immanants of constant width":
    also connected through other hyperedges:
      (none)
  Member "on the hardness of the noncommutative determinant":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "on explicit branching programs for the rectangular determinant and permanent polynomials")
  Member "arithmetic circuits and the hadamard product of polynomials":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "on explicit branching programs for the rectangular determinant and permanent polynomials")

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.CC(Computational Complexity)