相关论文: Another proof of undecidability for the correspond…

We consider a network coding setting where some of the messages and edges have fixed alphabet sizes, that do not change when we increase the common alphabet size of the rest of the messages and edges. We prove that the problem of deciding…

Since Cocke and Minsky proved 2-tag systems universal, they have been extensively used to prove the universality of numerous computational models. Unfortunately, all known algorithms give universal 2-tag systems that have a large number of…

Post Embedding Problems are a family of decision problems based on the interaction of a rational relation with the subword embedding ordering, and are used in the literature to prove non multiply-recursive complexity lower bounds. We refine…

Several physically inspired problems have been proven undecidable; examples are the spectral gap problem and the membership problem for quantum correlations. Most of these results rely on reductions from a handful of undecidable problems,…

Emil Post's tag system problem posed the question of whether or not a tag system $\{N=3, P(0) = 00, P(1) = 1101\}$ has a configuration, simulation of which will never halt or end up in a loop. Over the subsequent decades, there were several…

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…

In this letter, we revisit the {\em orbit problem}, which was studied in \cite{HAR69,SHA79,KL86}. In \cite{KL86}, Kannan and Lipton proved that this problem is decidable in polynomial time. In this paper, we study the {\em approximate orbit…

The undecidability of basic decision problems for general FIFO machines such as reachability and unboundedness is well-known. In this paper, we provide an underapproximation for the general model by considering only runs that are…

We discuss the accuracy of the attribution commonly given to Turing's 1936 paper "On computable numbers..." for the computable undecidability of the halting problem, coming eventually to a nuanced conclusion.

Decision problems in physics have been an active field of research for quite a few decades resulting in some interesting findings in recent years. However, such research investigations are based on a priori knowledge of theoretical computer…

We consider the new extension of population protocols with unordered data and show that the corresponding well-specification problem and therefore also other verification problems are undecidable.

Recently it was shown that it is undecidable whether a term rewrite system can be proved terminating by a polynomial interpretation in the natural numbers. In this paper we show that this is also the case when restricting the…

A probabilistic approach to the stable matching problem has been identified as an important research area with several important open problems. When considering random matchings, ex-post stability is a fundamental stability concept. A…

Roughly speaking, a recurrence relation is nested if it contains a subexpression of the form ... A(...A(...)...). Many nested recurrence relations occur in the literature, and determining their behavior seems to be quite difficult and…

This paper presents correspondence between Albert Einstein and the mathematical analyst J. L. B. Cooper on the Einstein-Podolsky-Rosen (EPR) paradox of quantum theory published in 1935. Two letters written by Cooper, and the replies from…

We establish the undecidability of 2019 puzzle game Baba is You through a reduction from the Post correspondence problem. In particular, we consider a restricted form of the Post correspondence problem introduced by Neary (arXiv:1312.6700)…

Roman Schnabel's article argues that the Einstein-Podolsky-Rosen (EPR) paradox can be resolved by identifying a flaw in what the author calls the "EPR implication" and by using radioactive alpha decay as an example showing that…

Transductions are binary relations of finite words. For rational transductions, i.e., transductions defined by finite transducers, the inclusion, equivalence and sequential uniformisation problems are known to be undecidable. In this paper,…

We resolve three long-standing open problems, namely the (algorithmic) decidability of network coding, the decidability of conditional information inequalities, and the decidability of conditional independence implication among random…

General potential theories concern the study of functions which are subharmonic with respect to a suitable constraint set (called a subequation) in the space of 2-jets. While interesting in their own right, general potential theories are…