Related papers: Musings on generic-case complexity

We define general linguistic intelligence as the ability to reuse previously acquired knowledge about a language's lexicon, syntax, semantics, and pragmatic conventions to adapt to new tasks quickly. Using this definition, we analyze…

A simple criterion is presented for a practical construction of generalized moments that allow one to approach the theoretical Rao-Cramer limit for parameter estimation while avoiding the complexity of the maximum likelihood method in the…

In this paper, we propose the frameworks of generalized performance evaluation and generalized controller synthesis. To this end, we give a true concurrent process calculus as the model of systems, and present a lattice-valued performance…

The concept of quantum complexity has far-reaching implications spanning theoretical computer science, quantum many-body physics, and high energy physics. The quantum complexity of a unitary transformation or quantum state is defined as the…

Length generalization refers to the ability to extrapolate from short training sequences to long test sequences and is a challenge for current large language models. While prior work has proposed some architecture or data format changes to…

A new class of functions is presented. The structure of the algorithm, particularly the selection criteria (branching), is used to define the fundamental property of the new class. The most interesting property of the new functions is that…

This thesis investigates the quality of randomly collected data by employing a framework built on information-based complexity, a field related to the numerical analysis of abstract problems. The quality or power of gathered information is…

This article surveys quantum computational complexity, with a focus on three fundamental notions: polynomial-time quantum computations, the efficient verification of quantum proofs, and quantum interactive proof systems. Properties of…

The complexity of quantum computation remains poorly understood. While physicists attempt to find ways to create quantum computers, we still do not have much evidence one way or the other as to how useful these machines will be. The tools…

Parameterized complexity theory offers a framework for a refined analysis of hard algorithmic problems. Instead of expressing the running time of an algorithm as a function of the input size only, running times are expressed with respect to…

Several machine learning problems arising in natural language processing can be modeled as a sequence labeling problem. We provide Gaussian process models based on pseudo-likelihood approximation to perform sequence labeling. Gaussian…

We introduce a class of information measures based on group entropies, allowing us to describe the information-theoretical properties of complex systems. These entropic measures are nonadditive, and are mathematically deduced from a series…

In this research we present a quantum circuit for estimating algorithmic complexity using the coding theorem method. This accelerates inferring algorithmic structure in data for discovering causal generative models. The computation model is…

Software code complexity is a well-studied property to determine software component health. However, the existing code complexity metrics do not directly take into account the fault-proneness aspect of the code. We propose a metric called…

This paper explores the problem of quantum measurement complexity. In computability theory, the complexity of a problem is determined by how long it takes an effective algorithm to solve it. This complexity may be compared to the difficulty…

The question What is Complexity? has occupied a great deal of time and paper over the last 20 or so years. There are a myriad different perspectives and definitions but still no consensus. In this paper I take a phenomenological approach,…

We describe the generic modules in each component of the spaces of representations of certain string algebras. In so doing, we calculate the dimensions of higher self-extension groups for generic modules. This algorithm lends itself for use…

Quantum circuit complexity-a measure of the minimum number of gates needed to implement a given unitary transformation-is a fundamental concept in quantum computation, with widespread applications ranging from determining the running time…

Qualitative data analysis provides insight into the underlying perceptions and experiences within unstructured data. However, the time-consuming nature of the coding process, especially for larger datasets, calls for innovative approaches,…

An approach for incorporating embedded simulation and analysis capabilities in complex simulation codes through template-based generic programming is presented. This approach relies on templating and operator overloading within the C++…