This paper addresses the problem of determining the distance between two regular languages. It will show how to expand Jaccard distance, which works on finite sets, to potentially-infinite regular languages. The entropy of a regular language plays a large role in the extension. Much of the paper is spent investigating the entropy of a regular language. This includes addressing issues that have required previous authors to rely on the upper limit of Shannon's traditional formulation of entropy, because its limit does not always exist. The paper also includes proposing a new limit based formulation for the entropy of a regular language and proves that formulation to both exist and be equivalent to Shannon's original formulation (when it exists). Additionally, the proposed formulation is shown to equal an analogous but formally quite different notion of topological entropy from Symbolic Dynamics -- consequently also showing Shannon's original formulation to be equivalent to topological entropy. Surprisingly, the natural Jaccard-like entropy distance is trivial in most cases. Instead, the entropy sum distance metric is suggested, and shown to be granular in certain situations.
Several regular language distance and similarity functions are suggested in @cite_10 . That paper constructs a natural R-tree-like index of regular expressions. The index allows for faster matching of a string against a large number of regular expressions. To construct the index, several distance functions are considered. These include a max-count measure, which considers the number of strings in both languages with length less than some constant to be the languages' similarity; a rate-of-growth measure, which divides the sum of strings sized @math to @math in one language by the sum of strings sized @math to @math in another language; and a minimum description length measure, which computes the number of bits needed to encode a path through an NFA.
@cite_10
2144221002 1998314653 2171313960 2131151781
A new class of distances appropriate for measuring similarity relations between sequences, say one type of similarity per distance, is studied. We propose a new "normalized information distance," based on the noncomputable notion of Kolmogorov complexity, and show that it is in this class and it minorizes every computable distance in the class (that is, it is universal in that it discovers all computable similarities). We demonstrate that it is a metric and call it the similarity metric . This theory forms the foundation for a new practical tool. To evidence generality and robustness, we give two distinctive applications in widely divergent areas using standard compression programs like gzip and GenCompress. First, we compare whole mitochondrial genomes and infer their evolutionary history. This results in a first completely automatic computed whole mitochondrial phylogeny tree. Secondly, we fully automatically compute the language tree of 52 different languages. We use an information-theoretic notion, namely, (Shannon) information rate, to generalize common syntactic similarity metrics (like Hamming distance and longest common subsequences) between strings to ones between languages. We show that the similarity metrics between two regular languages are computable. We further study self-similarity of a regular language under various similarity metrics. As far as semantic similarity is concerned, we study the amplitude of an automaton, which intuitively characterizes how much a typical execution of the automaton fluctuates. Finally, we investigate, through experiments, how to measure similarity between two real-world programs using Lempel-Ziv compression on the runs at the assembly level. ABSTRACT Measuring the similarity between words, sentences, paragraphs and documents is an important component in various tasks such as information retrieval, document clustering, word-sense disambiguation, automatic essay scoring, short answer grading, machine translation and text summarization. This survey discusses the existing works on text similarity through partitioning them into three approaches; String-based, Corpus-based and Knowledge-based similarities. Furthermore, samples of combination between these similarities are presented. General Terms Text Mining, Natural Language Processing. Keywords BasedText Similarity, Semantic Similarity, String-Based Similarity, Corpus-Based Similarity, Knowledge-Based Similarity. NeedlemanWunsch 1. INTRODUCTION Text similarity measures play an increasingly important role in text related research and applications in tasks Nsuch as information retrieval, text classification, document clustering, topic detection, topic tracking, questions generation, question answering, essay scoring, short answer scoring, machine translation, text summarization and others. Finding similarity between words is a fundamental part of text similarity which is then used as a primary stage for sentence, paragraph and document similarities. Words can be similar in two ways lexically and semantically. Words are similar lexically if they have a similar character sequence. Words are similar semantically if they have the same thing, are opposite of each other, used in the same way, used in the same context and one is a type of another. DistanceLexical similarity is introduced in this survey though different String-Based algorithms, Semantic similarity is introduced through Corpus-Based and Knowledge-Based algorithms. String-Based measures operate on string sequences and character composition. A string metric is a metric that measures similarity or dissimilarity (distance) between two text strings for approximate string matching or comparison. Corpus-Based similarity is a semantic similarity measure that determines the similarity between words according to information gained from large corpora. Knowledge-Based similarity is a semantic similarity measure that determines the degree of similarity between words using information derived from semantic networks. The most popular for each type will be presented briefly. This paper is organized as follows: Section two presents String-Based algorithms by partitioning them into two types character-based and term-based measures. Sections three and four introduce Corpus-Based and knowledge-Based algorithms respectively. Samples of combinations between similarity algorithms are introduced in section five and finally section six presents conclusion of the survey. We present an approach for the construction of text similarity functions using a parameterized resemblance coefficient in combination with a softened cardinality function called soft cardinality. Our approach provides a consistent and recursive model, varying levels of granularity from sentences to characters. Therefore, our model was used to compare sentences divided into words, and in turn, words divided into q-grams of characters. Experimentally, we observed that a performance correlation function in a space defined by all parameters was relatively smooth and had a single maximum achievable by "hill climbing." Our approach used only surface text information, a stop-word remover, and a stemmer to tackle the semantic text similarity task 6 at SEMEVAL 2012. The proposed method ranked 3rd (average), 5th (normalized correlation), and 15th (aggregated correlation) among 89 systems submitted by 31 teams.