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On Computational Limits of Modern Hopfield Models: A Fine-Grained Complexity Analysis
International Conference on Machine LearningWe investigate the computational limits of the memory retrieval dynamics of modern Hopfield models from the fine-grained complexity analysis. Our key contribution is the characterization of a phase transition behavior in the efficiency of all possible ...
Jerry Yao-Chieh Hu +3 more
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Complexity of Categorical Theories with Computable Models
Algebra and Logic, 2004The main results of the article are as follows: Theorem 1. For each natural number \(n\geq 1\), there exists an \(\aleph_1\)-categorical theory \(T\) of finite signature such that (1) the Turing degree of \(T\) equals \(\mathbf{0}^{(n)}\); (2) \(T\) has a computable model; (3) all countable models of \(T\) have computable isomorphic copies; (4) \(T ...
Goncharov, S. S., Khusainov, B. Kh.
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Complexity problems in computational theory
Russian Mathematical Surveys, 1981CONTENTS Introduction Chapter I. Methods of general computability theory in complexity bounds § 1. Complexity hierarchies. Complexity in finite domains § 2. Exponential and high lower bounds § 3. Complexity classes. Universal problems Chapter II. Methods and techniques for constructing "fast" algorithms § 1. Identification of subwords of a given word §
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The Existential Theory of the Reals as a Complexity Class: A Compendium
arXiv.orgWe survey the complexity class $\exists \mathbb{R}$, which captures the complexity of deciding the existential theory of the reals. The class $\exists \mathbb{R}$ has roots in two different traditions, one based on the Blum-Shub-Smale model of real ...
Marcus Schaefer +2 more
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Intrinsic theories and computational complexity
1995We introduce a new proof theoretic approach to computational complexity. With each free algebra \(\mathbb{A}\)we associate a first order “intrinsic theory for \(\mathbb{A}\)”, IT (\(\mathbb{A}\)), with no initial functions other than the constructors of \(\mathbb{A}\), and no axioms for them other than the generative and inductive axioms, which ...
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Computational Complexity and Recursion Theory
2010A general axiomatic approach to computational complexity was formulated by Blum [1]. His work was greatly influenced by the work of Rabin [23] and served to generalize to all complexity measures, results derived by Hartmanis and Sterns [8] for Turing machine computation times.
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Bridging the complexity gap in computational heterogeneous catalysis with machine learning
Nature Catalysis, 2023Tianyou Mou +7 more
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Computational Information Theory: Bridging Shannon's Information Theory and Computational Complexity
We develop Computational Information Theory as a comprehensive bridge between Claude Shannon’s classical information theory and computational complexity theory. Shannon’s framework addresses communication, data compression, and channel capacity, while complexity theory focuses on computational resources and problem difficulty.openaire +1 more source
Quantum computing and quantum complexity theory
2000 IEEE International Symposium on Circuits and Systems. Emerging Technologies for the 21st Century. Proceedings (IEEE Cat No.00CH36353), 2002There is strong evidence that computers based upon the principles of quantum physics represent an inherently new and more powerful model of computation. Such computers violate the modern form of the Church-Turing thesis (which lies at the foundations of computer science). This thesis can be informally summarized as follows: all physical implementations
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