Related papers: Pseudo-solutions of word equations
Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…
An improved finite difference method with compact correction term is proposed to solve the Poisson equations. The compact correction term is developed by a coupled high-order compact and low-order classical finite difference formulations.…
Tarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas iff a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may…
In this paper, we discuss the question whether a physical "simplification" of a model makes it always easier to study, at least from a mathematical and numerical point of view. To this end, we give different examples showing that these…
The notion of concept has been studied for centuries, by philosophers, linguists, cognitive scientists, and researchers in artificial intelligence (Margolis & Laurence, 1999). There is a large literature on formal, mathematical models of…
Several types of term rewriting systems can be distinguished by the way their rules overlap. In particular, we define the classes of prefix, suffix, bottom-up and top-down systems, which generalize similar classes on words. Our aim is to…
We introduce a new notion of "regularity structure" that provides an algebraic framework allowing to describe functions and / or distributions via a kind of "jet" or local Taylor expansion around each point. The main novel idea is to…
Using arch-jumping functions and properties of the arch factorization of words, we propose a new algorithm for computing the subword circular universality index of words. We also introduce the subword universality signature for words, that…
Continued fractions in the field of $p$--adic numbers have been recently studied by several authors. It is known that the real continued fraction of a positive quadratic irrational is eventually periodic (Lagrange's Theorem). It is still…
We consider the semiconjugate factorization and reduction of order for non-autonomous, nonlinear, higher order difference equations containing linear arguments. These equations have appeared in several mathematical models in biology and…
We present a novel approach to sentence simplification which departs from previous work in two main ways. First, it requires neither hand written rules nor a training corpus of aligned standard and simplified sentences. Second, sentence…
Consider the resolvent problem associated with the linearized viscous flow around a rotating body. Within a setting of classical Sobolev spaces, this problem is not well posed on the whole imaginary axis. Therefore, a framework of…
From Rauzy graph Rauzy Scheme can be obtaining by uniting sequence of vertices of ingoing and outgoing degree 1 by arches. This notion is a tool to describe Rauzy graph behavior. For morphic superword we prove periodicity of Rauzy schemes.…
Type-free systems of logic are designed to consistently handle significant instances of self-reference. Some consistent type-free systems also have the feature of allowing the sort of general abstraction or comprehension principle that…
We establish a consistency result by comparing two independent notions of generalised solutions to a large class of linear hyperbolic first order PDE systems with constant coefficients, showing that they eventually coincide. The first is…
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…
The long-standing problem of time in canonical quantum gravity is the source of several conceptual and technical issues. Here, recent mathematical results are used to provide a consistent algebraic formulation of dynamical symplectic…
The Massively Parallel Computation (MPC) model serves as a common abstraction of many modern large-scale data processing frameworks, and has been receiving increasingly more attention over the past few years, especially in the context of…
We introduce a notion of strong periodicity of a module over a finite-dimensional algebra over a field. We prove that the existence of such modules over certain idempotent algebras is both a necessary and sufficient condition for the…
Contexts are terms with one `hole', i.e. a place in which we can substitute an argument. In context unification we are given an equation over terms with variables representing contexts and ask about the satisfiability of this equation.…