Related papers: Computational Complexity of Interactive Behaviors
The complexity of cellular automata is traditionally measured by their computational capacity. However, it is difficult to choose a challenging set of computational tasks suitable for the parallel nature of such systems. We study the…
We propose a definition of quantum computable functions as mappings between superpositions of natural numbers to probability distributions of natural numbers. Each function is obtained as a limit of an infinite computation of a quantum…
Computability logic (CoL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently introduced semantical platform and ambitious program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth…
Emergent collective group processes and capabilities have been studied through analysis of transactive memory, measures of group task performance, and group intelligence, among others. In their approach to collective behaviors, these…
In this paper, we define a Mathematical model of program structure. Mathematical model of program structure defined here provides unified mathematical treatment of program structure, which reveals that a program is a large and finite set of…
How can complexity theory and algorithms benefit from practical advances in computing? We give a short overview of some prior work using practical computing to attack problems in computational complexity and algorithms, informally describe…
"Clarithmetic" is a generic name for formal number theories similar to Peano arithmetic, but based on computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html) instead of the more traditional classical or intuitionistic logics.…
The complexity of large-scale distributed systems, particularly when deployed in physical space, calls for new mechanisms to address composability and reusability of collective adaptive behaviour. Computational fields have been proposed as…
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…
The diversity of patterns that emerge from complex systems motivates their use for scientific or artistic purposes. When exploring these systems, the challenges faced are the size of the parameter space and the strongly non-linear mapping…
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…
Recent years have seen significant activity on the problem of using data for the purpose of learning properties of quantum systems or of processing classical or quantum data via quantum computing. As in classical learning, quantum learning…
With even the most trivial of applications now being written on top of millions of lines code of libraries, API's, and programming languages, much of the complexity that used to exist when designing software has been abstracted away to…
Form a pure mathematical point of view, common functional forms representing different physical phenomena can be defined. For example, rates of chemical reactions, diffusion and heat transfer are all governed by exponential-type…
The use of graphics processing units for scientific computations is an emerging strategy that can significantly speed up various different algorithms. In this review, we discuss advances made in the field of computational physics, focusing…
Formal explainability guarantees the rigor of computed explanations, and so it is paramount in domains where rigor is critical, including those deemed high-risk. Unfortunately, since its inception formal explainability has been hampered by…
We propose an extension of the framework for discussing the computational complexity of problems involving uncountably many objects, such as real numbers, sets and functions, that can be represented only through approximation. The key idea…
We introduce a formal definition of Wolfram's notion of computational process based on cellular automata, a physics-like model of computation. There is a natural classification of these processes into decidable, intermediate and complete.…
Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we…
Information flow framed in a computational and complexity context is relevant to the understanding of cognitive processes and awareness. In this paper, we begin with analyzing an information theory framework developed in recent years under…