Related papers: Nominal Unification Revisited
We introduce a first-order theory of finite full binary trees and then identify decidable and undecidable fragments of this theory. We show that the analogue of Hilbert`s 10th Problem is undecidable by constructing a many-to-one reduction…
We introduce nominal string diagrams as, string diagrams internal in the category of nominal sets. This requires us to take nominal sets as a monoidal category, not with the cartesian product, but with the separated product. To this end, we…
A new characterization of provably recursive functions of first-order arithmetic is described. Its main feature is using only terms consisting of 0, the successor S and variables in the quantifier rules, namely, universal elimination and…
We introduce a new Hopf algebra that operates on pairs of finite interval partitions and permutations of equal length. This algebra captures vincular patterns, which involve specifying both the permutation patterns and the consecutive…
We propose an equivalent formula for the higher-order derivatives used in the study of Generalized Almost Perfect Nonlinear functions over an arbitrary finite field of characteristic $p$. The result is obtained by counting the number of…
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
In this paper we investigate the parallelization of two modular algorithms. In fact, we consider the modular computation of Gr\"obner bases (resp. standard bases) and the modular computation of the associated primes of a zero-dimensional…
Disjoint union is a partial binary operation returning the union of two sets if they are disjoint and undefined otherwise. A disjoint-union partial algebra of sets is a collection of sets closed under disjoint unions, whenever they are…
A necessary and sufficient condition is provided for the solvability of a binomial congruence with a composite modulus, circumventing its prime factorization. This is a generalization of Euler's Criterion through that of Euler's Theorem,…
Binomial coefficients have been used for centuries in a variety of fields and have accumulated numerous definitions. In this paper, we introduce a new way of defining binomial coefficients as repeated sums of ones. A multitude of binomial…
Quantifier-elimination or model-completeness of the affine part of some classical first order theories are proved.
A unified explicit form for difference formulas to approximate the fractional and classical derivatives is presented. The formula gives finite difference approximations for any classical derivatives with a desired order of accuracy at nodal…
We investigate final coalgebras in nominal sets. This allows us to define types of infinite data with binding for which all constructions automatically respect alpha equivalence. We give applications to the infinitary lambda calculus.
Common meadows are commutative and associative algebraic structures with two operations (addition and multiplication) with additive and multiplicative identities and for which inverses are total. The inverse of zero is an error term…
We present several enumeration results holding in sets of words called neutral and which satisfy restrictive conditions on the set of possible extensions of nonempty words. These formulae concern return words and bifix codes. They…
We use type-theoretic techniques to present an algebraic theory of $\infty$-categories with strict units. Starting with a known type-theoretic presentation of fully weak $\infty$-categories, in which terms denote valid operations, we extend…
Computing modular coincidences can show whether a given substitution system, which is supported on a point lattice in R^d, consists of model sets or not. We prove the computatibility of this problem and determine an upper bound for the…
This paper introduces a novel anti-unification algorithm for the generalization of variadic structures with binders, designed as a flexible tool for structural code comparison. By combining nominal techniques for handling variable binding…
Given a first-order sentence, a model-checking computation tests whether the sentence holds true in a given finite structure. Data provenance extracts from this computation an abstraction of the manner in which its result depends on the…
Necessary and sufficient conditions are given for the similarity between two perturbations of the (backward) shift by rank one operators, under certain assumptions on the perturbations. The proof of similarity is based on an explicit…