Wikipedia Bot @wikibot 0

A bigram is a group of two consecutive words or tokens in a text. In natural language processing (NLP), bigrams are used to analyze and understand language patterns by looking at pairs of words that appear next to each other. For example, in the sentence "The cat sat on the mat," the bigrams would be: 1. The cat 2. cat sat 3. sat on 4. on the 5.

Boolean grammar is a formal system for describing and working with logical expressions using Boolean algebra. It utilizes the principles of Boolean logic, which involves variables that can take on binary values (true/false or 1/0) and operations such as AND, OR, and NOT. In the context of grammar, Boolean grammar can be used to construct logical sentences or expressions that adhere to certain syntactic rules. These rules define how variables and operators can be combined to form valid expressions.

The Brzozowski derivative is a mathematical concept used in automata theory and formal language theory. It provides a way to compute the derivative of a regular expression with respect to a particular symbol, which can help in constructing finite automata or in the analysis of regular languages. Given a regular expression, the Brzozowski derivative with respect to a symbol from the alphabet describes how the expression behaves when that symbol is encountered.

The Büchi-Elgot-Trakhtenbrot theorem is a result in the field of formal languages and automata theory, specifically concerning the expressiveness of certain types of logical systems and their relationship to automata. The theorem establishes a correspondence between regular languages and certain logical formulas, which is a significant topic in the study of the foundations of computer science, particularly in the areas of model checking and verification.

Categorical grammar is a type of formal grammar that is used in theoretical linguistics and computational linguistics. It is based on category theory, which is a branch of mathematics that deals with abstract structures and their relationships. Categorical grammars treat syntactic categories (like nouns, verbs, etc.) and constructs (like sentences) in terms of mathematical objects and morphisms (arrows) between them. In categorical grammar, the main idea is that grammatical structures can be represented as categories.

The Chomsky hierarchy is a classification of formal grammars based on their generative power, proposed by Noam Chomsky in the 1950s. It divides grammars into four levels, each with increasing expressive power.

Chomsky Normal Form (CNF) is a specific way of structuring context-free grammars (CFGs) in formal language theory. A context-free grammar is said to be in Chomsky Normal Form if all of its production rules meet one of the following criteria: 1. **A → BC**: A production rule where a single non-terminal symbol (A) produces exactly two non-terminal symbols (B and C).

The Chomsky–Schützenberger enumeration theorem is a result in formal language theory that provides a way to count the number of strings of a given length that can be generated by a context-free grammar (CFG). Specifically, it deals with the enumeration of strings in relation to the derivations of the grammar.

The Chomsky–Schützenberger representation theorem is a fundamental result in formal language theory, particularly in the study of context-free languages and their connections to formal grammars and automata. Named after Noam Chomsky and Marcel-Paul Schützenberger, the theorem characterizes certain classes of languages and relationships between different grammatical representations.

The "closest string" problem often refers to a computational problem in the realm of string processing or bioinformatics. It typically involves determining a string (or multiple strings) that is closest to a given string based on a defined metric, usually in terms of edit distance. The most commonly used metric for this purpose is the Levenshtein distance, which measures how many single-character edits (insertions, deletions, or substitutions) are required to change one string into another.

A **compact semigroup** is a mathematical structure that arises in the field of functional analysis and dynamical systems. To understand what a compact semigroup is, it's important to break down the concepts involved: 1. **Semigroup**: A semigroup is a set equipped with an associative binary operation.

Compiler Description Language (CDL) is a type of formal language used to define the syntax and semantics of programming languages, particularly in the context of compilers. CDL serves the purpose of providing a structured way to describe the components of a compiler, including grammar rules, parsing techniques, and various transformations that occur during compilation. CDL can take various forms and may include features for specifying: 1. **Syntax**: The structure of the programming language is often described using context-free grammars.

Concatenation is the operation of joining two or more strings or sequences end-to-end to form a single string or sequence. In programming and computer science, this is commonly used with text strings, but it can also apply to other data structures, such as lists or arrays.

In formal language theory, the term "cone" does not typically refer to a specific concept like it does in geometry. However, the term may pop up in various contexts related to formal languages, automata, and computational theory, often relating to sets of strings or languages and their properties.

The Conference on Implementation and Application of Automata (CIAA) is an academic conference that focuses on the theory, implementation, and applications of automata and formal languages. Automata are mathematical models of computation that are used to design and analyze algorithms and systems in computer science.

Conjunctive grammar is a formal grammar framework that extends traditional context-free grammars, primarily used in the field of computational linguistics and formal language theory. In conjunctive grammar, the productions (rules) allow the combination of multiple rules and conditions to generate strings in a more complex way than simple context-free grammars. The key feature of conjunctive grammars is their use of conjunctions in the grammar rules.

A **context-free grammar (CFG)** is a formal system used to define the syntax of programming languages, natural languages, and other formal languages. It consists of a set of production rules that describe how symbols can be combined to generate strings within a particular language. ### Components of a Context-Free Grammar: 1. **Terminals**: These are the basic symbols from which strings are formed. In programming languages, terminals might include keywords, operators, and punctuation.

A **context-free language (CFL)** is a type of formal language that can be generated by a context-free grammar (CFG). In formal language theory, context-free languages are significant because they can describe a wide range of syntactic structures used in programming languages and natural languages. ### Key Concepts: 1. **Context-Free Grammar (CFG)**: - A CFG consists of a set of production rules that define how symbols in the language can be replaced or transformed.

Context-sensitive grammar (CSG) is a type of formal grammar that is more powerful than context-free grammar (CFG) and is used in the field of formal language theory, a branch of computer science and linguistics. In a context-sensitive grammar, the production rules are sensitive to the context of non-terminal symbols. This means that the rules can add complexity to the generated strings based on the surrounding symbols.

A context-sensitive language (CSL) is a type of formal language that is defined by a context-sensitive grammar. Context-sensitive grammars are more powerful than context-free grammars and are used to describe languages that require context to determine their grammatical structure.