We introduce new classes of weighted automata on words. Equipped with pebbles and a two-way mechanism, they go beyond the class of recognizable formal power series, but capture a weighted version of first-order logic with bounded transitive closure. In contrast to previous work, this logic allows for unrestricted use of universal quantification. Our main result states that pebble weighted autom...

The degree of similarity or dissimilarity between the objects under study plays an important role. In vector space, especially, the cosine similarity measure is often used in information retrieval, citation analysis, and automatic classification. However, it scarcely deals with trapezoidal fuzzy information and multicriteria decision-making problems. For this purpose, a cosine similarity measur...

The paper aims to come up with a system that examines the degree of semantic equivalence between two sentences. At the core of the paper is the attempt to grade the similarity of two sentences by finding the maximal weighted bipartite match between the tokens of the two sentences. The tokens include single words, or multiwords in case of Named Entitites, adjectivally and numerically modified wo...

Indo-European languages are the native of habitants south and west Eurasia. It is largest spoken language family in world with 3.5 billion speakers, corresponding to 46% population. Kurdish English genetically related, belong same branch languages, believed have evolved from a common proto-language. Lexical Similarity measures similarity and/or difference between set words any given two languag...

Prior to the implementation of CO2 injection EOR projects, the screening evaluation of candidate reservoirs will promote the economic benefits of CO2 injection. Currently, a uniform screening method for CO2 miscible flooding does not exist. Based on more than 112 successfully implemented CO2 miscible flooding reservoirs, which was referred in 2010 Worldwide EOR Survey, and CO2 miscible flooding...

We first establish a law of large numbers and a convergence theorem in distribution to show the rate of convergence of the non-local means filter for removing Gaussian noise. We then introduce the notion of degree of similarity to measure the role of similarity for the non-local means filter. Based on the convergence theorems, we propose a patch-based weighted means filter for removing impulse ...