Related papers: The existence of a near-unanimity function is deci…

Recently it has been proved that, assuming that there is an almost disjoint family of cardinality (2^{\mathfrak c}) in (\mathfrak c) (which is assured, for instance, by either Martin's Axiom, or CH, or even $2^{<\mathfrak c=\mathfrak c$})…

A conjecture is given that, if true, could lead to an algorithm for computing definite sums of rational functions.

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…

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,…

Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that typically arise from applying decision rules…

We prove that the word problem is undecidable in functionally recursive groups, and that the order problem is undecidable in automata groups, even under the assumption that they are contracting.

We consider decision problems for relations over finite and infinite words defined by finite automata. We prove that the equivalence problem for binary deterministic rational relations over infinite words is undecidable in contrast to the…

Many logical properties are known to be undecidable for normal modal logics, with few exceptions such as consistency and coincidence with $\mathsf{K}$. This paper shows that the property of being a union-splitting in…

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…

We show that a finite group $G$ admitting an automorphism $\alpha$ such that the function $G\rightarrow G$, $g\mapsto g\alpha(g)$, is bijective is necessarily solvable.

We address the problem of finding necessary and sufficient conditions for an arbitrary group, not necessarily finite, to admit a faithful irreducible representation over an arbitrary field.

A new continuity for set-valued functions is introduced, and an existence theorem is proved for such continuous set-valued functions.

We show that the finite satisfiability problem for the unary negation fragment with arbitrary number of transitive relations is decidable and 2-ExpTime-complete. Our result actually holds for a more general setting in which one can require…

We show that the higher-order matching problem is decidable using a game-theoretic argument.

We prove undecidability for every positive relevant logic extending the system axiomatized by hypothetical syllogism, prefixing, and suffixing and contained in the logic of the semilattice frame $(P_{\mathrm{fin}}(\mathbb{N}), \cup,…

We establish several results on the word problem for just infinite groups. First, for finitely generated just infinite groups we show that the word problem is uniformly decidable for presentations with recursively enumerable sets of…

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…

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 the problem of reconstructing a function given its values on a set of points with finite density. We prove that with probability one, the values of an almost periodic function on a random array of points (with finite density)…

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…