Related papers: Computability and Complexity of Unconventional Com…
Is there any hope for quantum computing to challenge the Turing barrier, i.e. to solve an undecidable problem, to compute an uncomputable function? According to Feynman's '82 argument, the answer is {\it negative}. This paper re-opens the…
We study computable topological spaces and semicomputable and computable sets in these spaces. In particular, we investigate conditions under which semicomputable sets are computable. We prove that a semicomputable compact manifold $M$ is…
Computing is a high-level process of a physical system. Recent interest in non-standard computing systems, including quantum and biological computers, has brought this physical basis of computing to the forefront. There has been, however,…
There are several forms of irreducibility in computing systems, ranging from undecidability to intractability to nonlinearity. This paper is an exploration of the conceptual issues that have arisen in the course of investigating speed-up…
What is computable with limited resources? How can we verify the correctness of computations? How to measure computational power with precision? Despite the immense scientific and engineering progress in computing, we still have only…
To scrutinize notions of computation and time complexity, we introduce and formally define an interactive model for computation that we call it the \emph{computation environment}. A computation environment consists of two main parts: i) a…
Multi-objective unconstrained combinatorial optimization problems (MUCO) are in general hard to solve, i.e., the corresponding decision problem is NP-hard and the outcome set is intractable. In this paper we explore special cases of MUCO…
Novel computational paradigms may provide the blueprint to help solving the time and energy limitations that we face with our modern computers, and provide solutions to complex problems more efficiently (with reduced time, power consumption…
Nature often builds physical structures tailored for specific information processing tasks with computations encoded using diverse phenomena. These can sometimes outperform typical general-purpose computers. However, describing the…
This is the first of a series of papers in which we study deep computations (ultracomputations) and deep iterates, formalizing the ideas of "asymptotic limit" of computations and compositional iterates, respectively. In this first paper of…
The development of quantum computing technologies builds on the unique features of quantum physics while borrowing familiar principles from the design of conventional devices. We introduce the fundamental concepts required for designing and…
A remarkable new definition of a self-delimiting universal Turing machine is presented that is easy to program and runs very quickly. This provides a new foundation for algorithmic information theory. This new universal Turing machine is…
Neuromorphic computing is a non-von Neumann computing paradigm that performs computation by emulating the human brain. Neuromorphic systems are extremely energy-efficient and known to consume thousands of times less power than CPUs and…
Computational complexity is a core theory of computer science, which dictates the degree of difficulty of computation. There are many problems with high complexity that we have to deal, which is especially true for AI. This raises a big…
Planning energy production is a challenging task due to its cost-sensitivity, fast-moving energy markets, uncertainties in demand, and technical constraints of power plants. Thus, more complex models of this so-called \emph{unit commitment…
Both automatic program verification and program transformation are based on program analysis. In the past decade a number of approaches using various automatic general-purpose program transformation techniques (partial deduction,…
We analyze the possibility and efficiency of non-holonomic control over quantum devices with exponentially large number of Hilbert space dimensions. We show that completely controllable devices of this type can be assembled from elementary…
In the past four decades, the notion of quantum polynomial-time computability has been mathematically modeled by quantum Turing machines as well as quantum circuits. This paper seeks the third model, which is a quantum analogue of the…
Anyons obtained from a finite gauge theory have a computational power that depends on the symmetry group. The relationship between group structure and computational power is discussed in this paper. In particular, it is shown that anyons…
Computational complexity is examined using the principle of increasing entropy. To consider computation as a physical process from an initial instance to the final acceptance is motivated because many natural processes have been recognized…