Related papers: On effective undecidability and Post's problem

In this paper we consider propositional calculi, which are finitely axiomatizable extensions of intuitionistic implicational propositional calculus together with the rules of modus ponens and substitution. We give a proof of undecidability…

We introduce a first-order theory of finite full binary trees and then identify decidable and undecidable fragments of this theory. We show that the analogue of Hilbert`s 10th Problem is undecidable by constructing a many-to-one reduction…

The Regular Post Embedding Problem extended with partial (co)directness is shown decidable. This extends to universal and/or counting versions. It is also shown that combining directness and codirectness in Post Embedding problems leads to…

We discuss the question of if and how undecidability might be translatable into physics, in particular with respect to prediction and description, as well as to complementarity games.

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…

In 1946 Emil Leon Post (Bulletin of Amer. Math. Soc. 52 (1946), 264 - 268) defined a famous correspondence decision problem which is nowadays called the Post Correspondence Problem, and he proved that the problem is undecidable. In this…

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…

There are many ways we can not know. Even in systems that we created ourselves, as, for example, systems in mathematical logic, Go\"edel and Tarski's theorems impose limits on what we can know. As we try to speak of the real world, things…

Machine learning researchers and practitioners steadily enlarge the multitude of successful learning models. They achieve this through in-depth theoretical analyses and experiential heuristics. However, there is no known general-purpose…

This paper delves into the intersection of computational theory and music, examining the concept of undecidability and its significant, yet overlooked, implications within the realm of modern music composition and production. It posits that…

We study the effective versions of several notions related to incompleteness, undecidability and inseparability along the lines of Pour-El's insights. Firstly, we strengthen Pour-El's theorem on the equivalence between effective essential…

Here we continue with the ideas expressed in "On the strangeness of quantum mechanics" aiming to demonstrate more concretely how this philosophical outlook might be used as a key for resolving the measurement problem. We will address in…

This paper presents a theory of systemic undecidability, reframing incomputability as a structural property of systems rather than a localized feature of specific functions or problems. We define a notion of causal embedding and prove a…

We are lifting classical problems from single instances to regular sets of instances. The task of finding a positive instance of the combinatorial problem $P$ in a potentially infinite given regular set is equivalent to the so called…

In the past century many fundamental results on unpredictability, undecidability and uncertainty have compelled scientists to grapple with the idea that some questions may never be resolved within our current theories. While this…

Notions of unknown truths and unknowable truths are important in formal epistemology, which are related to each other in e.g. Fitch's paradox of knowability. Although there have been some logical research on the notion of unknown truths and…

After discussing two senses in which the notion of undecidability is used, we present a survey of undecidable decision problems arising in various branches of mathematics.

We consider expressions built up from binary relation names using the operators union, composition, and set difference. We show that it is undecidable to test whether a given such expression $e$ is finitely satisfiable, i.e., whether there…

Recent work by Faizal et al. (2025) claims that G\"odelian undecidability of non-algorithmic truths in our universe imply the impossibility of a formal, algorithmic simulation of the universe. This paper clarifies the distinction between…

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…