Related papers: Nominal Sets in Agda -- A Fresh and Immature Mecha…

We introduce Voevodsky's univalent foundations and univalent mathematics, and explain how to develop them with the computer system Agda, which is based on Martin-L\"of type theory. Agda allows us to write mathematical definitions,…

Session types have emerged as a powerful paradigm for structuring communication-based programs. They guarantee type soundness and session fidelity for concurrent programs with sophisticated communication protocols. As type soundness proofs…

The problem of mechanically formalizing and proving metatheoretic properties of programming language calculi, type systems, operational semantics, and related formal systems has received considerable attention recently. However, the dual…

We characterize the fixed sets of automorphisms of an arbitrary countable, arithmetically saturated structure.

Nominal abstract syntax is an approach to representing names and binding pioneered by Gabbay and Pitts. So far nominal techniques have mostly been studied using classical logic or model theory, not type theory. Nominal extensions to simple,…

We recently presented the so-called allagmatic method, which includes a system metamodel providing a framework for describing, modelling, simulating, and interpreting complex systems. Its development and programming was guided by…

Given a graph, we associate each edge with the transposition which exchanges the endvertices. Fixing a linear order on the edge set, we obtain a permutation of the vertices. D\'enes proved that the permutation is a full cyclic permutation…

In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of…

The periodic discrete Toda equation defined over finite fields has been studied. We obtained the finite graph structures constructed by the network of states where edges denote possible time evolutions. We simplify the graphs by introducing…

We continue investigating the structure of externally definable sets in NIP theories and preservation of NIP after expanding by new predicates. Most importantly: types over finite sets are uniformly definable; over a model, a family of…

Generalizations of numeration systems in which N is recognizable by a finite automaton are obtained by describing a lexicographically ordered infinite regular language L over a finite alphabet A. For these systems, we obtain a…

The present paper deals with permutations induced by tame automorphisms over finite fields. The first main result is a formula for determining the sign of the permutation induced by a given elementary automorphism over a finite field. The…

The principle behind algebraic language theory for various kinds of structures, such as words or trees, is to use a compositional function from the structures into a finite set. To talk about compositionality, one needs some way of…

We define a new invariant of finitely generated representations of a finite group, with coefficients in a commutative noetherian ring. This invariant uses group cohomology and takes values in the singularity category of the coefficient…

We construct the ordinary irreducible representations of the group of automorphisms of a finite rooted tree and we get a natural parametrization of them. To achieve this goals, we introduce and study the combinatorics of tree compositions,…

In this paper we develop a formalism for working with twisted realizations of vertex and conformal algebras. As an example, we study realizations of conformal algebras by twisted formal power series. The main application of our technique is…

In this paper, we explore the concept of modularity in first-order answer set programming (ASP). We introduce a new formalism called parametric modular logic programs, which allows defining subprograms with parameters and intensionality…

We generalise the termination method of higher-order polynomial interpretations to a setting with impredicative polymorphism. Instead of using weakly monotonic functionals, we interpret terms in a suitable extension of System F-omega. This…

An infinite permutation is a linear ordering of the set of non-negative integers. Generally, the properties of infinite permutations analogous to those of infinite words show some resemblances and some differences between permutations and…

We propose a formalism for representation of finite languages, referred to as the class of IDL-expressions, which combines concepts that were only considered in isolation in existing formalisms. The suggested applications are in natural…