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Formal language theory has recently been successfully employed to unravel the power of transformer encoders. This setting is primarily applicable in Natural Language Processing (NLP), as a token embedding function (where a bounded number of…
Designing complex engineered systems requires managing tightly coupled trade-offs between subsystem capabilities and resource requirements. Monotone co-design provides a compositional language for such problems, but its generality does not…
The Lyndon array stores, at each position of a word, the length of the longest maximal Lyndon subword starting at that position, and plays an important role in combinatorics on words, for example in the construction of fundamental data…
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…
Information, stored or transmitted in digital form, is often structured. Individual data records are usually represented as hierarchies of their elements. Together, records form larger structures. Information processing applications have to…
We study the topological entropy of hom tree-shifts and show that, although the topological entropy is not a conjugacy invariant for tree-shifts in general, it remains invariant for hom tree higher block shifts. In…
The expressive power of transformers over inputs of unbounded size can be studied through their ability to recognize classes of formal languages. In this paper, we establish exact characterizations of transformers with hard attention (in…
Bruyere and Carton lifted the notion of finite automata reading infinite words to finite automata reading words with shape an arbitrary linear order L. Automata on finite words can be used to represent infinite structures, the so-called…
A word-to-word function is continuous for a class of languages~$\mathcal{V}$ if its inverse maps $\mathcal{V}$_languages to~$\mathcal{V}$. This notion provides a basis for an algebraic study of transducers, and was integral to the…
Finite-state complexity is a variant of algorithmic information theory obtained by replacing Turing machines with finite transducers. We consider the state-size of transducers needed for minimal descriptions of arbitrary strings and, as our…
Heavily doped semiconductors have emerged as tunable low-loss plasmonic materials at mid-infrared frequencies. In this article we investigate nonlinear optical phenomena associated with high concentration of free electrons. We use a…
We investigate the expressivity and computational complexity of two modal logics on finite forests equipped with operators to reason on submodels. The logic ML(|) extends the basic modal logic ML with the composition operator | from static…
While learning models are typically studied for inputs in the form of a fixed dimensional feature vector, real world data is rarely found in this form. In order to meet the basic requirement of traditional learning models, structural data…
Looped Transformers provide advantages in parameter efficiency, computational capabilities, and generalization for reasoning tasks. However, their expressive power regarding function approximation remains underexplored. In this paper, we…
Finite-turn pushdown automata (PDA) are investigated concerning their descriptional complexity. It is known that they accept exactly the class of ultralinear context-free languages. Furthermore, the increase in size when converting…
We address the problem of complementing higher-order patterns without repetitions of existential variables. Differently from the first-order case, the complement of a pattern cannot, in general, be described by a pattern, or even by a…
We will describe a new superconductivity mechanism, proposed by the authors in [1], which is based on a topologically ordered ground state rather than on the usual Landau mechanism of spontaneous symmetry breaking. Contrary to anyon…
This paper provides a geometric characterization of subclasses of the regular languages. We use finite model theory to characterize objects like strings and trees as relational structures. Logical statements meeting certain criteria over…
Tree sets are abstract structures that can be used to model various tree-shaped objects in combinatorics. Finite tree sets can be represented by finite graph-theoretical trees. We extend this representation theory to infinite tree sets.…
In reactive synthesis, the goal is to automatically generate an implementation from a specification of the reactive and non-terminating input/output behaviours of a system. Specifications are usually modelled as logical formulae or automata…