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We construct meta-intransitive systems of independent random variables of any finite order from basic tuple of random variables which generalize intransitive dice. Under this construction, the equality of some linear functional is…
We study relationship among versions of the Knapsack Problem where variables take values in Z and the number of them is fixed. In particular, we construct a finitely presented group where the problem of solvability of exponential equations…
This paper considers the problem of testing whether there exists a solution satisfying certain non-negativity constraints to a linear system of equations. Importantly and in contrast to some prior work, we allow all parameters in the system…
Nowadays fairness issues have raised great concerns in decision-making systems. Various fairness notions have been proposed to measure the degree to which an algorithm is unfair. In practice, there frequently exist a certain set of…
We study the following decision problem: is the language recognized by a quantum finite automaton empty or non-empty? We prove that this problem is decidable or undecidable depending on whether recognition is defined by strict or non-strict…
We identify a decidable synthesis problem for a class of programs of unbounded size with conditionals and iteration that work over infinite data domains. The programs in our class use uninterpreted functions and relations, and abide by a…
Consider a high-dimensional linear regression problem, where the number of covariates is larger than the number of observations and the interest is in estimating the conditional variance of the response variable given the covariates. A…
We show that for two afii varieties over an arbitrary field of characteristic zero, there is no general form of an algorithm for checking the presence of an embedding of one algebraic variety in another. Moreover, we establish this for…
We show that the unification problem `is there a substitution instance of a given formula that is provable in a given logic?' is undecidable for basic modal logics K and K4 extended with the universal modality. It follows that the…
We consider the decidability of the verification problem of programs \emph{modulo axioms} --- that is, verifying whether programs satisfy their assertions, when the functions and relations it uses are assumed to interpreted by arbitrary…
We construct an example of a group $G = \mathbb{Z}^2 \times G_0$ for a finite abelian group $G_0$, a subset $E$ of $G_0$, and two finite subsets $F_1,F_2$ of $G$, such that it is undecidable in ZFC whether $\mathbb{Z}^2\times E$ can be…
Testing conditional independence between two random vectors given a third is a fundamental and challenging problem in statistics, particularly in multivariate nonparametric settings due to the complexity of conditional structures. We…
As inductive inference and machine learning methods in computer science see continued success, researchers are aiming to describe ever more complex probabilistic models and inference algorithms. It is natural to ask whether there is a…
Conditional independence plays a foundational role in database theory, probability theory, information theory, and graphical models. In databases, conditional independence appears in database normalization and is known as the (embedded)…
We study first-order logic (FO) over the structure consisting of finite words over some alphabet $A$, together with the (non-contiguous) subword ordering. In terms of decidability of quantifier alternation fragments, this logic is…
For each Turing machine T, we construct an algebra A'(T) such that the variety generated by A'(T) has definable principal subcongruences if and only if T halts, thus proving that the property of having definable principal subcongruences is…
This paper considers an extension of the linear non-Gaussian acyclic model (LiNGAM) that determines the causal order among variables from a dataset when the variables are expressed by a set of linear equations, including noise. In…
We provide a simple example showing that some conditional information inequalities (even in a weak form) cannot be derived from unconditional inequalities.
Parametric timed automata extend the standard timed automata with the possibility to use parameters in the clock guards. In general, if the parameters are real-valued, the problem of language emptiness of such automata is undecidable even…
Unmeasured confounding is a threat to causal inference and gives rise to biased estimates. In this article, we consider the problem of individualized decision-making under partial identification. Firstly, we argue that when faced with…