Related papers: Applications of Metric Coinduction
The goal of constraint-based sequence mining is to find sequences of symbols that are included in a large number of input sequences and that satisfy some constraints specified by the user. Many constraints have been proposed in the…
We study nested conditions, a generalization of first-order logic to a categorical setting, and provide a tableau-based (semi-decision) procedure for checking (un)satisfiability and finite model generation. This generalizes earlier results…
We show why and when entanglement is needed for quantum-enhanced precision measurements, and which type of entanglement is useful. We give a simple, intuitive construction that shows how entanglement transforms parallel estimation…
We argue that parameterized complexity is a useful tool with which to study global constraints. In particular, we show that many global constraints which are intractable to propagate completely have natural parameters which make them…
We introduce the notion of property signatures, a representation for programs and program specifications meant for consumption by machine learning algorithms. Given a function with input type $\tau_{in}$ and output type $\tau_{out}$, a…
This paper considers a simulation-based estimator for a general class of Markovian processes and explores some strong consistency properties of the estimator. The estimation problem is defined over a continuum of invariant distributions…
In classical estimation theory, the central limit theorem implies that the statistical error in a measurement outcome can be reduced by an amount proportional to n^(-1/2) by repeating the measures n times and then averaging. Using quantum…
In this paper, we introduce a new class of implicit function to prove common fixed point theorems in fuzzy metric space. Moreover we define a new altering distance in terms of integral and utilize the same to deduce integral type…
Recently many papers on cone metric spaces have been appeared, and main topological properties of such spaces have been obtained. A cone metric space is Hausdorff, and first countable, so the topology of it coincides with a topology induced…
Type theories with multi-clocked guarded recursion provide a flexible framework for programming with coinductive types encoding productivity in types. Combining this with solutions to general guarded domain equations one can also construct…
Up-to techniques' represent enhancements of the coinduction proof method and are widely used on coinductive behavioural relations such as bisimilarity. Abstract formulations of these coinductive techniques exist, using fixed-points or…
We develop a unified framework for nonlinear subdivision schemes on complete metric spaces (CMS). We begin with CMS preliminaries and formalize refinement in CMS, retaining key structural properties, such as locality. We prove a convergence…
Bove and Capretta's popular method for justifying function definitions by general recursive equations is based on the observation that any structured general recursion equation defines an inductive subset of the intended domain (the "domain…
Transportation distances have been used for more than a decade now in machine learning to compare histograms of features. They have one parameter: the ground metric, which can be any metric between the features themselves. As is the case…
Following a review of metric, ultrametric and generalized ultrametric, we review their application in data analysis. We show how they allow us to explore both geometry and topology of information, starting with measured data. Some themes…
We introduce the concept of protometric and present some properties of protometrics.
Inductive proofs can be represented as proof schemata, i.e. as parameterized sequences of proofs defined in a primitive recursive way. Applications of proof schemata can be found in the area of automated proof analysis where the schemata…
We introduce real induction, a proof technique analogous to mathematical induction but applicable to statements indexed by an interval on the real line. More generally we give an inductive principle applicable in any Dedekind complete…
There are two basic ways of weakening the definition of the well-known metric regularity property by fixing one of the points involved in the definition. The first resulting property is called metric subregularity and has attracted a lot of…
A metric algebra is a metric variant of the notion of $\Sigma$-algebra, first introduced in universal algebra to deal with algebras equipped with metric structures such as normed vector spaces. In this paper, we showed metric versions of…