Related papers: Reducts of Ramsey structures
We contribute to a recent research program which aims at revisiting the study of the complexity of word problems, a major area of research in combinatorial algebra, through the lens of the theory of computably enumerable equivalence…
The attempt is to give a formal concpet of system, and with this provide a definition of category, that will also satisfy the definition of a system. An axiomatic base is given, for constructing the group of integers. In the process, we…
As countless examples show, it can be fruitful to study a sequence of complicated objects all at once via the formalism of generating functions. We apply this point of view to the homology and combinatorics of orbit configuration spaces:…
We present a new, category theoretic point of view on finite Ramsey theory. Our aims are as follows: -- to define the category theoretic notions needed for the development of finite Ramsey Theory, -- to state, in terms of these notions, the…
The theory of finite term algebras provides a natural framework to describe the semantics of functional languages. The ability to efficiently reason about term algebras is essential to automate program analysis and verification for…
We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…
Infinite types and formulas are known to have really curious and unsound behaviors. For instance, they allow to type {\Omega}, the auto- autoapplication and they thus do not ensure any form of normalization/productivity. Moreover, in most…
This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…
The general setting of this work is the constraint-based synthesis of termination arguments. We consider a restricted class of programs called lasso programs. The termination argument for a lasso program is a pair of a ranking function and…
We propose the first framework for defining relational program logics for arbitrary monadic effects. The framework is embedded within a relational dependent type theory and is highly expressive. At the semantic level, we provide an…
To any finite ordered subset and any finite partition of a group a set of tuples of positive integers, named as configurations, is associated that describes the group's behavior. The present paper provides an exposition of this notion and…
Predicate logic is the premier choice for specifying classes of relational structures. Homomorphisms are key to describing correspondences between relational structures. Questions concerning the interdependencies between these two means of…
We study a new notion of reduction between structures called enumerable functors related to the recently investigated notion of computable functors. Our main result shows that enumerable functors and effective interpretability with the…
We prove that the existence of finite combinatorial objects such as affine planes, mutually orthogonal Latin squares, and resolvable balanced incomplete block designs can be reformulated as the existence of certain algorithmic reductions…
In this series of papers, we investigate properties of a finite group which are determined by its low degree irreducible representations over a number field $F$, i.e. its representations on matrix rings $\operatorname{M}_n(D)$ with $n \leq…
We prove that for any homogeneous structure $\mathbf{K}$ in a language with finitely many relation symbols of arity at most two satisfying SDAP$^+$ (or LSDAP$^+$), there are spaces of subcopies of $\mathbf{K}$, forming subspaces of the…
A first-order structure $M$ is said to have the infinite sunflower property if, for each $k \in \mathbb{N}_+$ and each structure $M' \cong M$ whose elements are $k$-sets, there is $S \subseteq M'$, $S \cong M$, such that $S$ is a sunflower:…
We deal with first-order definability in the substructure ordering $(\mathcal{D}; \sqsubseteq)$ of finite directed graphs. In two papers, the author has already investigated the first-order language of the embeddability ordering $(…
One of the main reasons for the correspondence of regular languages and monadic second-order logic is that the class of regular languages is closed under images of surjective letter-to-letter homomorphisms. This closure property holds for…
Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on…