Related papers: Undecidability everywhere?
Sources of predictability in the basic laws of physics are described in the most general theoretical context -- the quantum theory of the universe as a whole. (To appear in the Proceedings of the conference on Fundamental Sources of…
The blog has several entries on group theory interacting with computability and wider logic, several open questions, and an entry on undecidability in physics.
We prove that arithmetic is interpretable in any indecomposable polynomial ring (in any set of variables), and in addition we provide an alternative uniform proof of undecidability for all members in this class of rings.
We look for a deep connection between mathematics and physics. Our approach is to propose a set theory T which leads to a concise mathematical description of physical fields and to a finite unit of action. The concept of "definability" of…
Can a problem undecidable with classical resources be decidable with quantum ones? The answer expected is no; as both being Turing theories, they should not solve the Halting problem - a problem unsolvable by any Turing machine. Yet, we…
A description of physical reality in which wholeness is the foundation is discussed along with the motivation for such an attempt. As a possible mathematical framework within which a physical theory based on wholeness may be expressed,…
Several examples are used to illustrate how we deal cavalierly with infinities and unphysical systems in physics. Upon examining these examples in the context of infinities from Cantor's theory of transfinite numbers, the only known…
We study the difficulty of computing topological entropy of subshifts subjected to mixing restrictions. This problem is well-studied for multidimensional subshifts of finite type : there exists a threshold in the irreducibility rate where…
LECTURE GIVEN AT TH2002. Given a set of Boolean variables, and some constraints between them, is it possible to find a configuration of the variables which satisfies all constraints? This problem, which is at the heart of combinatorial…
The study of word equations (or the existential theory of equations over free monoids) is a central topic in mathematics and theoretical computer science. The problem of deciding whether a given word equation has a solution was shown to be…
We propose a rigorous decomposition of predictive error, highlighting that not all 'irreducible' error is genuinely immutable. Many domains stand to benefit from iterative enhancements in measurement, construct validity, and modeling. Our…
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…
We propose an interpretation of physics named potentiality realism. This view, which can be applied to classical as well as to quantum physics, regards potentialities (i.e. intrinsic, objective propensities for individual events to obtain)…
The notion of geometric version of an infinitely divisible law is introduced. Concepts parallel to attraction and partial attraction are developed and studied in the setup of geometric summing of random variables.
We study the problem of completely automatically verifying uninterpreted programs---programs that work over arbitrary data models that provide an interpretation for the constants, functions and relations the program uses. The verification…
This article discusses the possibility of predicting human behavior in a mechanism. Such a mechanism will have certain properties, which are defined and discussed here. Here it is shown that, unfortunately, certain property combinations are…
This paper surveys main and recent studies on temporal logics in a broad sense by presenting various logic systems, dealing with various time structures, and discussing important features, such as decidability (or undecidability) results,…
We prove that the problems of representing a finite ordered complemented semigroup or finite lattice-ordered semigroup as an algebra of binary relations over a finite set are undecidable. In the case that complementation is taken with…
Reliable uncertainty quantification is essential for the use of machine learning in physics, where scientific discoveries depend on validated probabilistic statements. We provide a structured overview of uncertainty quantification in ML for…
In this manuscript we present a detailed proof for undecidability of the equivalence of finite substitutions on regular language $b\{0,1\}^*c$. The proof is based on the works of Leonid P. Lisovik.