Related papers: Definability Results for Top-Down Tree Transducers

We answer an open question in the theory of transducer degrees initially posed in [1] on the existence of a diamond structure in the transducer hierarchy. Transducer degrees are the equivalence classes formed by word transformations which…

We propose to study transformations on graphs, and more generally structures, by looking at how the cut-rank (as introduced by Oum) of subsets is affected when going from the input structure to the output structure. We consider…

We address an open question of Francis and Steel about phylogenetic networks and trees. They give a polynomial time algorithm to decide if a phylogenetic network, N, is tree-based and pose the problem: given a fixed tree T and network N, is…

For finite q, we classify the countable, descendant-homogeneous digraphs in which the descendant set of any vertex is a q-valent tree. We also give conditions on a rooted digraph G which allow us to construct a countable…

For a nonautonomous linear system with nonuniform contraction, we construct a topological equivalence between this system and an unbounded nonlinear perturbation. This topological equivalence is constructed as a composition of…

In the setting of constructive mathematics, we suggest and study a framework for decidability of properties, which allows for finer distinctions than just "decidable, semidecidable, or undecidable". We work in homotopy type theory and use…

Algorithms for learning decision trees often include heuristic local-search operations such as (1) adjusting the threshold of a cut or (2) also exchanging the feature of that cut. We study minimizing the number of classification errors by…

The transformer neural network has significantly out-shined all other neural network architectures as the engine behind large language models. We provide a theoretical analysis of the expressivity of the transformer architecture through the…

We provide decidability and undecidability results on the model-checking problem for infinite tree structures. These tree structures are built from sequences of elements of infinite relational structures. More precisely, we deal with the…

Functional transductions realized by two-way transducers (equivalently, by streaming transducers and by MSO transductions) are the natural and standard notion of "regular" mappings from words to words. It was shown recently (LICS'13) that…

Without any means of interpretation, neural networks that predict molecular properties and bioactivities are merely black boxes. We will unravel these black boxes and will demonstrate approaches to understand the learned representations…

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…

We consider labelings of a finite regular tree by a finite alphabet subject to restrictions specified by a nonnegative transition matrix, propose an algorithm for determining whether the set of possible configurations on the last row of the…

We study the approximation of high-dimensional rank one tensors using point evaluations and consider deterministic as well as randomized algorithms. We prove that for certain parameters (smoothness and norm of the $r$th derivative) this…

We study the intrinsic transformation of feature maps across convolutional network layers with explicit top-down control. To this end, we develop top-down feature transformer (TFT), under controllable parameters, that are able to account…

The notion of non-deterministic logical matrix (where connectives are interpreted as multi-functions) preserves many good properties of traditional semantics based on logical matrices (where connectives are interpreted as functions) whilst…

We suggest a compositional vector representation of parse trees that relies on a recursive combination of recurrent-neural network encoders. To demonstrate its effectiveness, we use the representation as the backbone of a greedy, bottom-up…

High-dimensional policies, such as those represented by neural networks, cannot be reasonably interpreted by humans. This lack of interpretability reduces the trust users have in policy behavior, limiting their use to low-impact tasks such…

We demonstrate that the question whether or not a given postcritically finite topological ramified covering map of the 2-sphere is Thurston equivalent to a rational map is algorithmically decidable.

Consider the following heuristic for building a decision tree for a function $f : \{0,1\}^n \to \{\pm 1\}$. Place the most influential variable $x_i$ of $f$ at the root, and recurse on the subfunctions $f_{x_i=0}$ and $f_{x_i=1}$ on the…