Related papers: On effective undecidability and Post's problem
Senizergues has proved that language equivalence is decidable for disjoint epsilon-deterministic PDA. Stirling has showed that strong bisimilarity is decidable for PDA. On the negative side Srba demonstrated that the weak bisimilarity is…
Using recent machine learning results that present an information-theoretic perspective on underfitting and overfitting, we prove that deciding whether an encodable learning algorithm will always underfit a dataset, even if given unlimited…
Stackelberg equilibria have become increasingly important as a solution concept in computational game theory, largely inspired by practical problems such as security settings. In practice, however, there is typically uncertainty regarding…
We construct an existentially undecidable complete discretely valued field of mixed characteristic with existentially decidable residue field and decidable algebraic part, answering a question by Anscombe-Fehm in a strong way. Along the…
We construct a finitely presented group with undecidable word problem and with Dehn function bounded by a quadratic function on an infinite set of positive integers.
We show that including degrees of a particular kind of provability in the search target for any theorem-prover in sufficiently powerful formal systems over finite-sized statements preserves well-definition and a sufficient consistency while…
Our main result is the equivalence of two notions of reducibility between structures. One is a syntactical notion which is an effective version of interpretability as in model theory, and the other one is a computational notion which is a…
In this paper, we investigate the structure of the most general kind of substitution shifts, including non-minimal ones, and allowing erasing morphisms. We prove the decidability of many properties of these morphisms with respect to the…
It was noticed by Harel in [Har86] that "one can define $\Sigma_1^1$-complete versions of the well-known Post Correspondence Problem". We first give a complete proof of this result, showing that the infinite Post Correspondence Problem in a…
A typical kind of question in mathematical logic is that for the necessity of a certain axiom: Given a proof of some statement $\phi$ in some axiomatic system $T$, one looks for minimal subsystems of $T$ that allow deriving $\phi$. In…
We consider the decidability of state-to-state reachability in linear time-invariant control systems over continuous time. We analyse this problem with respect to the allowable control sets, which are assumed to be the image under a linear…
Infinite games where several players seek to coordinate under imperfect information are known to be intractable, unless the information flow is severely restricted. Examples of undecidable cases typically feature a situation where players…
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.
I investigate the question whether G\"odel's undecidability theorems play a crucial role in the search for a unified theory of physics. I conclude that unless the structure of space-time is fundamentally discrete we can never decide whether…
In 1964, Paul Erd\H{o}s published a paper settling a question about function spaces that he had seen in a problem book. Erd\H{o}s proved that the answer was yes if and only if the continuum hypothesis was false: an innocent-looking question…
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…
This is a systematic review of the concept of indistinguishability in both classical and quantum mechanics, with particular attention to Gibbs' paradox. Section 1 is on the Gibbs paradox; section 2 is a defense of the concept of classical…
We show that satisfiability for CTL* with equality-, order-, and modulo-constraints over Z is decidable. Previously, decidability was only known for certain fragments of CTL*, e.g., the existential and positive fragments and EF.
A connection between the state estimation problem and the separability problem is noticed and exploited to find efficient numerical algorithms to solve the first one. Based on these ideas, we also derive a systematic method to obtain upper…
An axiomatics for indistinguishability of elementary particles in terms of hidden variables is presented in a manner which depart from the standard approaches usually given to hidden variables. Quantum distribution functions are also…