Related papers: Essential Hereditary Undecidability
We introduce the class of synchronous subsequential relations, a subclass of the synchronous relations which embodies some properties of subsequential relations. If we take relations of this class as forming the possible transitions of an…
Recently, we have shown that satisfiability for $\mathsf{ECTL}^*$ with constraints over $\mathbb{Z}$ is decidable using a new technique. This approach reduces the satisfiability problem of $\mathsf{ECTL}^*$ with constraints over some…
In this paper, we investigate a conjecture by von Haeseler concerning the Maximum Parsimony method for phylogenetic estimation, which was published by the Newton Institute in Cambridge on a list of open phylogenetic problems in 2007. This…
We consider the general problem of sensitive and specific discrimination between biochemical species. An important instance is immune discrimination between self and not-self, where it is also observed experimentally that ligands just below…
Session types are behavioural types for guaranteeing that concurrent programs are free from basic communication errors. Recent work has shown that asynchronous session subtyping is undecidable. However, since session types have become…
Over the past decade, the low-degree heuristic has been used to estimate the algorithmic thresholds for a wide range of average-case planted vs null distinguishing problems. Such results rely on the hypothesis that if the low-degree moments…
The decidability of the reachability problem for finitary PCF has been used as a theoretical basis for fully automated verification tools for functional programs. The reachability problem, however, often becomes undecidable for a slight…
We introduce (weak) oddomorphisms of graphs which are homomorphisms with additional constraints based on parity. These maps turn out to have interesting properties (e.g., they preserve planarity), particularly in relation to homomorphism…
We present an intuitive geometrical entanglement criterion. It allows formulation of simple and experimentally friendly sufficient conditions for entanglement. The conditions are illustrated with several examples. Moreover, a generalization…
Uniformly finite homology is a coarse invariant for metric spaces; in particular, it is a quasi-isometry invariant for finitely generated groups. In this article, we study uniformly finite homology of finitely generated amenable groups and…
We investigate the nonparametric, composite hypothesis testing problem for arbitrary unknown distributions in the asymptotic regime where both the sample size and the number of hypotheses grow exponentially large. Such asymptotic analysis…
This paper belongs to the research on the limit of the first incompleteness theorem. Effectively inseparable theories (EI) can be viewed as an effective version of essentially undecidable theories (EU), and EI is stronger than EU. We…
We develop some basic results about full amalgamation classes with intrinsic trascendentals. These classes have generics whose models may have finite subsets whose intrinsic closure is not contained in its algebraic closure. We will show…
An $h$-ary relation $\r$ on a finite set $A$ is said to be \emph{hereditarily rigid} if the unary partial functions on $A$ that preserve $\r$ are the subfunctions of the identity map or of constant maps. A family of relations ${\mathcal F}$…
To date, there has been no formal study of the statistical cost of interpretability in machine learning. As such, the discourse around potential trade-offs is often informal and misconceptions abound. In this work, we aim to initiate a…
We use a generalization of a construction by Ziegler to show that for any field $F$ and any countable collection of countable subsets $A_i \subseteq F, i \in \calI \subset \Z_{>0}$ there exist infinitely many fields $K$ of arbitrary…
Infinite games with imperfect information are known to be undecidable unless the information flow is severely restricted. One fundamental decidable case occurs when there is a total ordering among players, such that each player has access…
Multilingual language models achieve strong aggregate performance yet often behave unpredictably across languages, scripts, and cultures. We argue that mechanistic explanations for such models should satisfy a \emph{causal} standard: claims…
We establish the undecidability of conditional affine information inequalities, the undecidability of the conditional independence implication problem with a constraint that one random variable is binary, and the undecidability of the…
In the paper hereditary classes of ${\rm L}$-structures are studied with language of the form ${{\rm L} = {\rm L_{fin}} \cup {\rm L_\infty}}$, where ${{\rm L_{fin}} = \langle R_1,R_2,\ldots, R_m, = \rangle}$ and ${{\rm L_\infty} = \langle…