Related papers: Pseudo-solutions of word equations
We describe the design of a quantifier elimination framework for the complex numbers in the language of ordered rings supplemented with symbols for the imaginary unit, real parts, imaginary parts, and conjugates. Technically, we use a…
We proof a uniqueness and periodicity theorem for bounded solutions of uniformly elliptic equations in certain unbounded domains.
Uniform proofs are sequent calculus proofs with the following characteristic: the last step in the derivation of a complex formula at any stage in the proof is always the introduction of the top-level logical symbol of that formula. We…
We consider several novel aspects of unique factorization in formal languages. We reprove the familiar fact that the set uf(L) of words having unique factorization into elements of L is regular if L is regular, and from this deduce an…
We set up a parametrised monadic translation for a class of call-by-value functional languages, and prove a corresponding soundness theorem. We then present a series of concrete instantiations of our translation, demonstrating that a number…
Emerging computational paradigms, such as probabilistic and hybrid programming, introduce new primitive operations that often need to be combined with classic programming constructs. However, it still remains a challenge to provide a…
We introduce "synchronous algebras", an algebraic structure tailored to recognize automatic relations (aka. synchronous relations, or regular relations). They are the equivalent of monoids for regular languages, however they conceptually…
We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using…
Conceptual combination performs a fundamental role in creating the broad range of compound phrases utilized in everyday language. This article provides a novel probabilistic framework for assessing whether the semantics of conceptual…
In this short survey we describe recent advances on word equations with non-rational constraints in groups and monoids, highlighting the important role that formal languages play in this area.
Repetition avoidance has been studied since Thue's work. In this paper, we considered another type of repetition, which is called pseudo-power. This concept is inspired by Watson-Crick complementarity in DNA sequence and is defined over an…
The purpose of this short paper is to identify the mathematical essence of the superiorization methodology. This methodology has been developed in recent years while attempting to solve specific application-oriented problems. Consequently,…
An analysis using classical stochastic processes is used to construct a consistent system of quantum counterfactual reasoning. When applied to a counterfactual version of Hardy's paradox, it shows that the probabilistic character of quantum…
We establish a generalization of the p-adic local monodromy theorem (of Andre, Mebkhout, and the author) in which differential equations on rigid analytic annuli are replaced by differential equations on so-called fake annuli. The latter…
In this article, we examine how clausal resolution can be applied to a specific, but widely used, non-classical logic, namely discrete linear temporal logic. Thus, we first define a normal form for temporal formulae and show how arbitrary…
This work is devoted to the study of the existence and periodicity of solutions of initial differential problems, paying special attention to the explicit computation of the period. These problems are also connected with some particular…
We study formal languages which are capable of fully expressing quantitative probabilistic reasoning and do-calculus reasoning for causal effects, from a computational complexity perspective. We focus on satisfiability problems whose…
We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.
We introduce a novel variant of logical relations that maps types not merely to partial equivalence relations on values, as is commonly done, but rather to a proof-relevant generalisation thereof, namely setoids. The objects of a setoid…
In this paper we give a framework for describing how abstract systems can be used to compute if no randomness or error is involved. Using this we describe a class of classical "physical" computation systems whose computational capabilities…