Related papers: Normal basises and symbolical dynamics
Existential rules are an expressive knowledge representation language mainly developed to query data. In the literature, they are often supposed to be in some normal form that simplifies technical developments. For instance, a common…
This survey paper is aimed to describe a relatively new branch of symbolic dynamics which we call Arithmetic Dynamics. It deals with explicit arithmetic expansions of reals and vectors that have a "dynamical" sense. This means precisely…
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…
The definition of stable models for propositional formulas with infinite conjunctions and disjunctions can be used to describe the semantics of answer set programming languages. In this note, we enhance that definition by introducing a…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
We consider forkable regular expressions, which enrich regular expressions with a fork operator, to establish a formal basis for static and dynamic analysis of the communication behavior of concurrent programs. We define a novel…
Let A be an alphabet and W be a set of words in the free monoid A*. Let S(W) denote the Rees quotient over the ideal of A* consisting of all words that are not subwords of words in W. We call a set of words W finitely based if the monoid…
The theory of substitution sequences and their higher-dimensional analogues is intimately connected with symbolic dynamics. By systematically studying the factors (in the sense of dynamical systems theory) of a substitution dynamical…
Dendric shift spaces simultaneously generalize codings of regular interval exchanges and episturmian shift spaces, themselves both generalizations of Sturmian words. One of the key properties enforced by dendricity is the Return Theorem. In…
The article treats the geometrical theory of partial differential equations in the absolute sense, i.e., without any additional structures and especially without any preferred choice of independent and dependent variables. The equations are…
In this paper, we use a categorical and functorial set up to model the syntax and inference of logics with algebraic signature, extending previous works on algebraisation of logics. The main feature of this work is that structurality, or…
A necessary and sufficient condition for an element of an algebra (in the sense of Universal Algebra) to be in the dominion of a subalgebra is given, in terms of transferable sets. This criterion is then used to formulate a more wieldy…
Our goal is to define an algebraic language for reasoning about non-deterministic computations. Towards this goal, we introduce an algebra of string-to-string transductions. Specifically, it is an algebra of partial functions on words over…
Symbolic dynamics is partly the study of walks in a directed graph. By a walk, here we mean a morphism to the graph from the Cayley graph of the monoid of non-negative integers. Sets of these walks are also important in other areas, such as…
Five algebraic notions of termination are formalised, analysed and compared: wellfoundedness or Noetherity, L\"ob's formula, absence of infinite iteration, absence of divergence and normalisation. The study is based on modal semirings,…
We develop techniques at the interface between differential algebra and model theory to study the following problems of exponential algebraicity: Does a given algebraic differential equation admits an exponentially algebraic solution, that…
We extend our formulation of Merge and Minimalism in terms of Hopf algebras to an algebraic model of a syntactic-semantic interface. We show that methods adopted in the formulation of renormalization (extraction of meaningful physical…
Starting with a combinatorial partition theorem for words over an infinite alphabet dominated by a fixed sequence, established recently by the authors, we prove recurrence results for topological dynamical systems indexed by such words. In…
We introduce an algebraic analogue of dynamical systems, based on term rewriting. We show that a recursive function applied to the output of an iterated rewriting system defines a formal class of models into which all the main architectures…
We study substitutive systems generated by nonprimitive substitutions and show that transitive subsystems of substitutive systems are substitutive. As an application we obtain a complete characterisation of the sets of words that can appear…