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: "on the hardness of almost sure termination"
  Abstract: This paper considers the computational hardness of computing expected outcomes and deciding (universal) (positive) almost-sure termination of probabilistic programs. It is shown that computing lower and upper bounds of expected outcomes is $\Sigma_1^0$- and $\Sigma_2^0$-complete, respectively. Deciding (universal) almost-sure termination as well as deciding whether the expected outcome of a program equals a given rational value is shown to be $\Pi^0_2$-complete. Finally, it is shown that deciding (universal) positive almost-sure termination is $\Sigma_2^0$-complete ($\Pi_3^0$-complete).

Connected through hyperedge HE-1 (induced by source paper "aiming low is harder inductive proof rules for lower bounds on weakest preexpectations in probabilistic program verification"):
  with members:
    - "quantitative separation logic a logic for reasoning about probabilistic pointer programs"
    - "on the termination problem for probabilistic higher order recursive programs"
    - "bounded expectations resource analysis for probabilistic programs"
    - "termination of nondeterministic recursive probabilistic programs"
    - "finding polynomial loop invariants for probabilistic programs"
    - "a new proof rule for almost sure termination"
    - "a weakest pre expectation semantics for mixed sign expectations"
    - "healthiness from duality"

Connected through hyperedge HE-2 (induced by source paper "computing expected runtimes for constant probability programs"):
  with members:
    - "termination of triangular integer loops is decidable"
    - "automated recurrence analysis for almost linear expected runtime bounds"
    - "bounded expectations resource analysis for probabilistic programs"
    - "a new proof rule for almost sure termination"
    - "lexicographic ranking supermartingales an efficient approach to termination of probabilistic programs"
    - "weakest precondition reasoning for expected run times of probabilistic programs"
    - "on termination of integer linear loops"
    - "minimizing expected termination time in one counter markov decision processes"

Connected through hyperedge HE-3 (induced by source paper "new approaches for almost sure termination of probabilistic programs"):
  with members:
    - "bounded expectations resource analysis for probabilistic programs"
    - "termination of nondeterministic recursive probabilistic programs"
    - "a new proof rule for almost sure termination"
    - "lexicographic ranking supermartingales an efficient approach to termination of probabilistic programs"
    - "a new rule for almost certain termination of probabilistic and demonic programs"
    - "termination analysis of probabilistic programs through positivstellensatz s"
    - "weakest precondition reasoning for expected run times of probabilistic programs"
    - "reasoning about recursive probabilistic programs"

Connected through hyperedge HE-4 (induced by source paper "on the termination problem for probabilistic higher order recursive programs"):
  with members:
    - "branching processes for quickcheck generators"
    - "on probabilistic term rewriting"
    - "a convenient category for higher order probability theory"
    - "a new proof rule for almost sure termination"
    - "relational semantics of linear logic and higher order model checking"
    - "complexity of model checking recursion schemes for fragments of the modal mu calculus"
    - "church a language for generative models"
    - "proving termination of probabilistic programs using patterns"

Connected through hyperedge HE-5 (induced by source paper "on probabilistic term rewriting"):
  with members:
    - "modular runtime complexity analysis of probabilistic while programs"
    - "bounded expectations resource analysis for probabilistic programs"
    - "a new proof rule for almost sure termination"
    - "termination analysis of probabilistic programs through positivstellensatz s"
    - "nagoya termination tool"
    - "church a language for generative models"
    - "on constructor rewrite systems and the lambda calculus"
    - "efficient csl model checking using stratification"

Connected through hyperedge HE-6 (induced by source paper "almost sure productivity"):
  with members:
    - "a new proof rule for almost sure termination"
    - "lexicographic ranking supermartingales an efficient approach to termination of probabilistic programs"
    - "coalgebraic trace semantics for continuous probabilistic transition systems"
    - "proving termination of probabilistic programs using patterns"
    - "data oblivious stream productivity"

Connected through hyperedge HE-7 (induced by source paper "how long o bayesian network will i sample thee a program analysis perspective on expected sampling times"):
  with members:
    - "a tutorial on learning with bayesian networks"
    - "a weakest pre expectation semantics for mixed sign expectations"
    - "weakest precondition reasoning for expected run times of probabilistic programs"

Connected through hyperedge HE-8 (induced by source paper "finding polynomial loop invariants for probabilistic programs"):
  with members:
    - "termination analysis of probabilistic programs through positivstellensatz s"
    - "synthesizing probabilistic invariants via doob s decomposition"
    - "counterexample guided polynomial loop invariant generation by lagrange interpolation"
    - "generating non linear interpolants by semidefinite programming"
    - "proving inequalities and solving global optimization problems via simplified cad projection"

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)