Chomsky Normal Form (CNF) is a standardized form of context-free grammars where each production rule is either of the form A → BC or A → a, with A, B, and C being non-terminal symbols and a being a terminal symbol. This form simplifies the parsing process and is particularly useful for algorithms like the CYK algorithm, which checks membership of strings in context-free languages.

Chomsky Normal Form

Context-Free Grammars (CFGs) are formal systems used to define the syntax of programming languages and natural languages, allowing the generation of strings from a set of production rules. They are essential in the design of compilers and interpreters, enabling the parsing and analysis of language constructs through a hierarchy of grammatical structures.

context-free grammars

A production rule is a fundamental component of formal grammar systems, used to describe how symbols in a language can be transformed or rewritten. It is essential in defining the syntax of programming languages and plays a critical role in parsing and compiling processes.

production rule

non-terminal symbols

In formal language theory and computer science, a terminal symbol is a basic, indivisible unit of a language's alphabet that appears in the strings generated by a grammar. Unlike non-terminal symbols, which are used to define the language's syntax and can be replaced, terminal symbols are the actual characters or tokens that appear in the final output of a language's derivation process.

terminal symbol

parsing process

The CYK Algorithm is a parsing algorithm for context-free grammars, particularly useful for determining whether a given string can be generated by a specific grammar. It operates using dynamic programming and is efficient for grammars in Chomsky Normal Form, making it a staple in computational linguistics and compiler design.

CYK algorithm

membership of strings

Context-free languages are a class of formal languages that can be generated by context-free grammars, which are used to describe the syntax of programming languages and natural languages. They are recognized by pushdown automata, making them more powerful than regular languages but less powerful than context-sensitive languages.

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