相关论文: Resource Limited Theories and their Extensions
Our purpose is to give an account of the $r$-tuple problem on the increasing sequence of reduced fractions having denominators bounded by a certain size and belonging to a fixed real interval. We show that when the size grows to infinity,…
Quantum resource theory is a cutting-edge tool used to study practical implementations of quantum mechanical principles under realistic operational constraints. It does this by modelling quantum systems as restricted classes of possible or…
This article discusses completeness of Boolean Algebra as First Order Theory in Goedel's meaning. If Theory is complete then any possible transformation is equivalent to some transformation using axioms, predicates etc. defined for this…
In addition to the important role of contextuality in foundations of quantum theory, this intrinsically quantum property has been identified as a potential resource for quantum advantage in different tasks. It is thus of fundamental…
The law of proportionate growth simply states that the time dependent change of a quantity $x$ is proportional to $x$. Its applicability to a wide range of dynamic phenomena is based on various assumptions for the proportionality factor,…
In this paper, we examine the limit of applicability of G\"{o}del's first incompleteness theorem ($\sf G1$ for short). We first define the notion "$\sf G1$ holds for the theory $T$". This paper is motivated by the following question: can we…
We present an adequacy theorem for a concurrent extension of probabilistic GCL. The underlying denotational semantics is based on the so-called mixed powerdomains, which combine non-determinism with probabilistic behaviour. The theorem…
The algorithmic theory of randomness is well developed when the underlying space is the set of finite or infinite sequences and the underlying probability distribution is the uniform distribution or a computable distribution. These…
A new concept of internal time (viewed as a scalar temporal field) is introduced which allows one to solve the energy problem in General Relativity. The law of energy conservation means that the total energy density of the full system of…
Nonlinear models and optimization methods have successfully tackled a rapidly growing set of problems in recent years. Indeed, a relatively small toolbox of such models and methods can provide sufficient performance across a large landscape…
A fundamental approach for the characterization and quantification of all kinds of resources is to study the conversion between different resource objects under certain constraints. Here we analyze, from a resource-non-specific standpoint,…
The "Law of the Minimum" states that growth is controlled by the scarcest resource (limiting factor). This concept was originally applied to plant or crop growth (Justus von Liebig, 1840) and quantitatively supported by many experiments.…
The randomization of a complete first order theory $T$ is the complete continuous theory $T^R$ with two sorts, a sort for random elements of models of $T$, and a sort for events in an underlying probability space. We study various notions…
Five-vectors theory of gravity is proposed, which admits an arbitrary choice of the energy density reference level. This theory is formulated as the constraint theory, where the Lagrange multipliers turn out to be restricted to some class…
To facilitate the design and optimization of nanomaterials for a given application it is necessary to understand the relationship between structure and physical properties. For large nanomaterials, there is imprecise structural information…
A fundamental problem in science is how to make logical inferences from scientific data. Mere data does not suffice since additional information is necessary to select a domain of models or hypotheses and thus determine the likelihood of…
Relative motion in space with multifractal time (fractional dimension of time close to integer $d_{t}=1+\epsilon (r,t), \epsilon \ll 1$) for "almost" inertial frames of reference (time is almost homogeneous and almost isotropic) is…
The WAY theorem establishes an important constraint that conservation laws impose on quantum mechanical measurements. We formulate the WAY theorem in the broader context of resource theories, where one is constrained to a subset of quantum…
I begin by examining the question of the quantum limits of knowledge by briefly presenting the constraints of the theory that derive from its mathematical structure (in particular the no-go theorems formulated by von Neumann and Kochen and…
Stephen Wolfram has recently outlined an unorthodox, multicomputational approach to fundamental theory, encompassing not only physics but also mathematics in a structure he calls The Ruliad, understood to be the entangled limit of all…