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We investigate the isomorphism problem in the setting of definable sets (equivalent to sets with atoms): given two definable relational structures, are they related by a definable isomorphism? Under mild assumptions on the underlying…
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…
Arbitrary Arrow Update Logic is a dynamic modal logic that uses an arbitrary arrow update modality to quantify over all arrow updates. Some properties of this logic have already been established, but until now it remained an open question…
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 wish to test whether a real-valued variable $Z$ has explanatory power, in addition to a multivariate variable $X$, for a binary variable $Y$. Thus, we are interested in testing the hypothesis $\mathbb{P}(Y=1\, | \, X,Z)=\mathbb{P}(Y=1\,…
A major challenge in estimating treatment effects in observational studies is the reliance on untestable conditions such as the assumption of no unmeasured confounding. In this work, we propose an algorithm that can falsify the assumption…
We consider entailment problems involving powerful constraint languages such as frontier-guarded existential rules in which we impose additional semantic restrictions on a set of distinguished relations. We consider restricting a relation…
The dynamical behavior of switched affine systems is known to be more intricate than that of the well-studied switched linear systems, essentially due to the existence of distinct equilibrium points for each subsystem. First, under…
Variance in predictions across different trained models is a significant, under-explored source of error in fair binary classification. In practice, the variance on some data examples is so large that decisions can be effectively arbitrary.…
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…
We solve a well known, long-standing open problem in relational databases theory, showing that the conjunctive query determinacy problem (in its "unrestricted" version) is undecidable.
We prove that the uniform recurrence of morphic sequences is decidable. For this we show that the number of derived sequences of uniformly recurrent morphic sequences is bounded. As a corollary we obtain that uniformly recurrent morphic…
We study forced oscillations on differentiable manifolds which are globally defined as the zero set of appropriate smooth maps in some Euclidean spaces. Given a T-periodic perturbative forcing field, we consider the two different scenarios…
We give a necessary and sufficient condition on a $d$-dimensional affine subspace of $\mathbb{R}^n$ to be characterized by a finite set of patterns which are forbidden to appear in its digitization. This can also be stated in terms of local…
We study systems of polynomial equations in infinite finitely generated commutative associative rings with an identity element. For each such ring $R$ we obtain an interpretation by systems of equations of a ring of integers $O$ of a finite…
We propose a new conditional dependence measure and a statistical test for conditional independence. The measure is based on the difference between analytic kernel embeddings of two well-suited distributions evaluated at a finite set of…
The deterministic membership problem for timed automata asks whether the timed language recognised by a nondeterministic timed automaton can be recognised by a deterministic timed automaton. We show that the problem is decidable when the…
Behavioural and neural time series are often correlated with the past. This history-dependence may represent a fundamental property of the measured variables, or may arise from how confounding variables change over time. Here we argue that…
Classical integrability is investigated for affine Toda field theories in the presence of a constant background tensor field. This leads to a further set of discrete possibilities for integrable boundary conditions depending upon the…
We prove decidability results on the existence of constant subsequences of uniformly recurrent morphic sequences along arithmetic progressions. We use spectral properties of the subshifts they generate to give a first algorithm deciding…