Related papers: On Reversible Transducers
Visibly pushdown transducers form a subclass of pushdown transducers that (strictly) extends finite state transducers with a stack. Like visibly pushdown automata, the input symbols determine the stack operations. In this paper, we prove…
We use tilting modules to study the structure of the tensor product of two simple modules for the algebraic group $\SL_2$, in positive characteristic, obtaining a twisted tensor product theorem for its indecomposable direct summands.…
Permutation rational functions over finite fields have attracted high interest in recent years. However, only a few of them have been exhibited. This article studies a class of permutation rational functions constructed using trace maps on…
We introduce the notions of semi-uniform input-to-state stability and its subclass, polynomial input-to-state stability, for infinite-dimensional systems. We establish a characterization of semi-uniform input-to-state stability based on…
Neural networks are widely used as a model for classification in a large variety of tasks. Typically, a learnable transformation (i.e. the classifier) is placed at the end of such models returning a value for each class used for…
Over the past few years, deep learning methods have proved to be of great interest for the computational fluid dynamics community, especially when used as surrogate models, either for flow reconstruction, turbulence modeling, or for the…
We study implicit reasoning, i.e. the ability to combine knowledge or rules within a single forward pass. While transformer-based large language models store substantial factual knowledge and rules, they often fail to compose this knowledge…
This paper studies data-driven stabilization of a class of unknown polynomial systems using data corrupted by bounded noise. Existing work addressing this problem has focused on designing a controller and a Lyapunov function so that a…
Top-down tree transducers are a convenient formalism for describing tree transformations. They can be equipped with regular look-ahead, which allows them to inspect a subtree before processing it. In certain cases, such a look-ahead can be…
Quantum theory is awash in multidimensional integrals that contain exponentials in the integration variables, their inverses, and inverse polynomials of those variables. The present paper introduces a means to reduce pairs of such integrals…
This paper develops an extension of infinite-dimensional backstepping method for parabolic and hyperbolic systems in one spatial dimension with two actuators. Typically, PDE backstepping is applied in 1-D domains with an actuator at one…
Automatic structures are first-order structures whose universe and relations can be represented as regular languages. It follows from the standard closure properties of regular languages that the first-order theory of an automatic structure…
For any truncated path algebra $\Lambda$ of a quiver, we classify, by way of representation-theoretic invariants, the irreducible components of the parametrizing varieties $\mathbf{Rep}_{\mathbf{d}}(\Lambda)$ of the $\Lambda$-modules with…
A language is dense if the set of all infixes (or subwords) of the language is the set of all words. Here, it is shown that it is decidable whether the language accepted by a nondeterministic Turing machine with a one-way read-only input…
Given a singular hypersurface in a regular 2-dimensional scheme essentially of finite type over a field, we construct an embedded resolution of singularities by weighted blow-ups. This differs from our earlier work which required…
We study the problem of learning to stabilize unknown noisy Linear Time-Invariant (LTI) systems on a single trajectory. It is well known in the literature that the learn-to-stabilize problem suffers from exponential blow-up in which the…
Pattern recognition based on a high-dimensional predictor is considered. A classifier is defined which is based on a Transformer encoder. The rate of convergence of the misclassification probability of the classifier towards the optimal…
Pebble transducers are nested two-way transducers which can drop marks (named "pebbles") on their input word. Such machines can compute functions whose output size is polynomial in the size of their input. They can be seen as simple…
We consider input-deterministic finite state transducers with infinite inputs and infinite outputs, and we consider the property of Borel normality on infinite words. When these transducers are given by a strongly connected set of states,…
Phase transitions mark qualitative reorganizations of collective behavior, yet identifying their boundaries remains challenging whenever analytic solutions are absent and conventional simulations fail. Here we introduce learnability as a…