Related papers: Exceeding Computational Complexity Trial-and-Error…

Mathematical Selection is a method in which we select a particular choice from a set of such. It have always been an interesting field of study for mathematicians. Combinatorial optimisation is the practice of selecting the best constituent…

This paper covers two topics: first an introduction to Algorithmic Complexity Theory: how it defines probability, some of its characteristic properties and past successful applications. Second, we apply it to problems in A.I. - where it…

Complexity is an interdisciplinary concept which, first of all, addresses the question of how order emerges out of randomness. For many reasons matrices provide a very practical and powerful tool in approaching and quantifying the related…

We survey results on the formalization and independence of mathematical statements related to major open problems in computational complexity theory. Our primary focus is on recent findings concerning the (un)provability of complexity…

Depth is a complexity measure for natural systems of the kind studied in statistical physics and is defined in terms of computational complexity. Depth quantifies the length of the shortest parallel computation required to construct a…

The study of the fundamental limits of information systems is a central theme in information theory. Both the traditional analytical approach and the recently proposed computational approach have significant limitations, where the former is…

Data-driven algorithm design is a paradigm that uses statistical and machine learning techniques to select from a class of algorithms for a computational problem an algorithm that has the best expected performance with respect to some…

Complexity theory is a useful tool to study computational issues surrounding the elicitation of preferences, as well as the strategic manipulation of elections aggregating together preferences of multiple agents. We study here the…

Many real-world dynamic systems, both natural and artificial, are understood to be performing computations. For artificial dynamic systems, explicitly designed to perform computation - such as digital computers - by construction, we can…

Computational thinking is a new problem soling method named for its extensive use of computer science techniques. It synthesizes critical thinking and existing knowledge and applies them in solving complex technological problems. The term…

We consider a class of optimization problems defined by a system of linear equations with min and max operators. This class of optimization problems has been studied under restrictive conditions, such as, (C1) the halting or stability…

Deep neural networks (DNN) have been widely used and play a major role in the field of computer vision and autonomous navigation. However, these DNNs are computationally complex and their deployment over resource-constrained platforms is…

We recall from previous work a model-independent framework of computational complexity theory. Notably for the present paper, the framework allows formalization of the issues of precision that present themselves when one considers physical,…

Technology is currently ubiquitous and is also part of the educational system at all levels. It started with communication technology systems, and later continued with digital competence. Nowadays, although these previous concepts are still…

Human societies continuously transform scattered information into collective judgments and coordinated action, whether through markets discovering prices, governments allocating resources, communities enforcing norms, or science converging…

We propose a decision-theoretic framework for computational complexity, complementary to classical theory: moving from syntactic exactness (Turing / Shannon) to semantic simulability (Le Cam). While classical theory classifies problems by…

Trying to be effective (no matter who exactly and in what field) a person face the problem which inevitably destroys all our attempts to easily get to a desired goal. The problem is the existence of some insuperable barriers for our mind,…

In three-dimensional computational topology, the theory of normal surfaces is a tool of great theoretical and practical significance. Although this theory typically leads to exponential time algorithms, very little is known about how these…

The study of Complex Systems is considered by many to be a new scientific field, and is distinguished by being a discipline that has applications within many separate areas of scientific study. The study of Neural Networks, Traffic…

Computational creativity is an emerging branch of artificial intelligence that places computers in the center of the creative process. Broadly, creativity involves a generative step to produce many ideas and a selective step to determine…