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We prove that the subsets of N^d that are S-recognizable for all abstract numeration systems S are exactly the 1-recognizable sets. This generalizes a result of Lecomte and Rigo in the one-dimensional setting.
We introduce sequentially $S_r$ modules over a commutative graded ring and sequentially $S_r$ simplicial complexes. This generalizes two properties for modules and simplicial complexes: being sequentially Cohen-Macaulay, and satisfying…
In Monoidal Computer I, we introduced a categorical model of computation where the formal reasoning about computability was supported by the simple and popular diagrammatic language of string diagrams. In the present paper, we refine and…
The asynchronous systems f are multi-valued functions, representing the non-deterministic models of the asynchronous circuits from the digital electrical engineering. In real time, they map an 'admissible input' function…
This thesis details a project to define a fully compositional theory of synchronous sequential circuits built from primitive components, motivated by applying techniques successfully used in programming languages to hardware. The first part…
Abstract separation systems provide a simple general framework in which both tree-shape and high cohesion of many combinatorial structures can be expressed, and their duality proved. Applications range from tangle-type duality and tree…
In this paper, we study the solving degrees for affine semi-regular sequences and their homogenized sequences. Some of our results are considered to give mathematically rigorous proofs of the correctness of methods for computing Gr\"{o}bner…
When people learn mathematical patterns or sequences, they are able to identify the concepts (or rules) underlying those patterns. Having learned the underlying concepts, humans are also able to generalize those concepts to other numbers,…
Let $\mathscr{A}$ be a nonempty set of infinite matrices of linear operators between two topological vector spaces. We show that a sequence is uniformly $\mathscr{A}$-summable if and only if it is $B$-summable for all matrices $B$ of linear…
Algebraic characterizations of the computational aspects of functions defined over the real numbers provide very effective tool to understand what computability and complexity over the reals, and generally over continuous spaces, mean. This…
The regular spanners (characterised by vset-automata) are closed under the algebraic operations of union, join and projection, and have desirable algorithmic properties. The core spanners (introduced by Fagin, Kimelfeld, Reiss, and…
Let $(A,B)$ be a pair of skew-symmetric matrices over a field of characteristic not 2. Its regularization decomposition is a direct sum \[ (\underline{\underline A},\underline{\underline B})\oplus (A_1,B_1)\oplus\dots\oplus(A_t,B_t) \] that…
We develop a (co)algebraic framework to study a family of process calculi with monadic branching structures and recursion operators. Our framework features a uniform semantics of process terms and a complete axiomatisation of semantic…
Scientists, engineers, biologists, and technology specialists universally leverage image segmentation to extract shape ensembles containing many thousands of curves representing patterns in observations and measurements. These large curve…
We prove that a sequence satisfying a certain symmetry property is $2$-regular in the sense of Allouche and Shallit, i.e., the $\mathbb{Z}$-module generated by its $2$-kernel is finitely generated. We apply this theorem to develop a general…
We introduce the notion of pattern for numerical semigroups, which allows us to generalize the definition of Arf numerical semigroups. In this way infinitely many other classes of numerical semigroups are defined giving a classification of…
We see how nested sequents, a natural generalisation of hypersequents, allow us to develop a systematic proof theory for modal logics. As opposed to other prominent formalisms, such as the display calculus and labelled sequents, nested…
A different route to identification of time-invariant linear systems has been recently proposed which does not require committing to a specific parametric model structure. Impulse responses are described in a nonparametric Bayesian…
First we define a new kind of function over $\mathbb{N}$. For each $i\in\mathbb{N}$ we have an associated function, which will be called $S_i$ . Then we define a new kind of sequence, to be made from the functions $S_i$ . Finally, we will…
In 2012, Meyer introduced the notions of generalized almost periodic measure and almost periodic pattern and proved that regular model sets in Euclidean space are almost periodic patterns. Here, we prove the converse in a slightly more…