An Unsolvable Problem of Elementary Number Theory

By A. Church. 1936

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Citations in the corpus

Deep learning in neural networks: An overview (2014, methodology): “and Obermayer, K. (2005). Sequence classific ation for protein analysis.”
PowerPlay: Training an Increasingly General Problem Solver by Continually Searching for the Simplest Still Unsolvable Problem (2011, neutral): “Assume the architecture of the solver is a universal computer (Gödel, 1931; Church, 1936; Post, 1936; Turing, 1936).”
On Learning to Think: Algorithmic Information Theory for Novel Combinations of Reinforcement Learning Controllers and Recurrent Neural World Models (2015, background): “Given some universal programming language [67, 35, 282, 194] for a universal computer, the algorithmic information content or Kolmogorov complexity of some computable object is the length of the shortest program that computes it.”
One Big Net For Everything (2018, background): “To become a general problem solver that is able to run arbitrary problem-solving programs, the controller of a robot or an artiﬁcial agent must be a general-purpose computer [15, 7, 92, 44].”
Quantifier Elimination and Cylindrical Algebraic Decomposition (2004, unknown): “See (Godel 1931), (Church 1936), and (Rosser 1936).”
The Gremlin graph traversal machine and language (invited talk) (2015, unknown): “5 A Primordial Graph Traversal Machine This section describes, at a high-level, a vision of graph co mputing that is, in many ways, analogous to the token rewrite mode l of the lambda calculus [4].”
Algorithmic Pseudorandomness in Quantum Setups. (2014, methodology): “The ﬁeld emerged in the 1930s with the independent works of Alan Turing [6] and Alonzo Church [7] who introduced two equivalent formalizations of the intuitive concept of algorithm .”
Harnessing the Power of the Second Quantum Revolution (2020, methodology): “Together with Church [40], they abstracted computers from the machines themselves, to state that all reasonable models of computation were essentially equivalent and could be mapped to a universal Turing machine (the Church-Turing thesis).”