Related papers: On a Crucial Problem in Probabilities and Solution

We describe a mathematical language for determining all possible patterns of contextuality in the dependence of stochastic outputs of a system on its deterministic inputs. The central notion is that of all possible couplings for…

Kolmogorov complexity theory is used to tell what the algorithmic informational content of a string is. It is defined as the length of the shortest program that describes the string. We present a programming language that can be used to…

Classical probability theory supports probability measures, assigning a fixed positive real value to each event, these measures are far from satisfactory in formulating real-life occurrences. The main innovation of this paper is the…

We prove that the equivalence of two fundamental problems in the theory of computing. For every polynomial $t(n)\geq (1+\varepsilon)n, \varepsilon>0$, the following are equivalent: - One-way functions exists (which in turn is equivalent to…

There is much interest in providing probabilistic semantics for defaults but most approaches seem to suffer from one of two problems: either they require numbers, a problem defaults were intended to avoid, or they generate peculiar side…

We consider the value 1 problem for probabilistic automata over finite words: it asks whether a given probabilistic automaton accepts words with probability arbitrarily close to 1. This problem is known to be undecidable. However, different…

What would be the consequences if there were fundamental limits to our ability to experimentally explore the world? In this work we seriously consider this question. We assume the existence of statements whose truth value is not…

Diverse applications of Kolmogorov complexity to learning [CIKK16], circuit complexity [OPS19], cryptography [LP20], average-case complexity [Hir21], and proof search [Kra22] have been discovered in recent years. Since the running time of…

We introduce the notion of a probabilistic measure which takes values in hyperbolic numbers and which satisfies the system of axioms generalizing directly Kolmogorov's system of axioms. We show that this new measure verifies the usual…

We perform the analysis of probabilistic assumptions of Bell's approach. We emphasize that J. Bell wrote about probability without to specify the concrete axiomatics of probability theory. The careful analysis demonstrated that…

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…

No theory of physics has been collectively scientifically verified in an experiment so far. It is pointed out that probabilistic structure of quantum theory can be collectively scientifically verified in an experiment. It is also argued…

We lay the groundwork for a formal framework that studies scientific theories and can serve as a unified foundation for the different theories within physics. We define a scientific theory as a set of verifiable statements, assertions that…

It is well-known that the law of total probability does not hold in general in quantum theory. However, the recent arguments on some of the fundamental assumptions in quantum theory based on the extended Wigner's Friend scenario show a need…

We present an impossibility result, called a theorem about facts and words, which pertains to a general communication system. The theorem states that the number of distinct words used in a finite text is roughly greater than the number of…

Goedel Incompleteness Theorem leaves open a way around it, vaguely perceived for a long time but not clearly identified. (Thus, Goedel believed informal arguments can answer any math question.) Closing this loophole does not seem obvious…

The familiar theories of physics have the feature that the application of the theory to make predictions in specific circumstances can be done by means of an algorithm. We propose a more precise formulation of this feature --- one based on…

Amplitudes are the major logical object in Quantum Theory. Despite this fact they presents no physical reality and in consequence only observables can be experimetally checked. We discuss the possibility of a theory of Quantum Probabilities…

We show that by taking into account randomness of realization of experimental contexts it is possible to construct common Kolmogorov space for data collected for these contexts, although they can be incompatible. We call such a construction…

The principal goal of this paper is to pass all quantum probability formulas to the projective space associated to the complex Hilbert space of a given quantum system, providing a more complete geometrization of quantum theory. Quantum…