Formal Languages Questions Medium
A context-free grammar is a formal system used to describe the syntax or structure of a formal language. It consists of a set of production rules that define how symbols can be combined to form valid strings in the language. These production rules typically have the form of a non-terminal symbol on the left-hand side, followed by an arrow, and then a sequence of symbols (both terminal and non-terminal) on the right-hand side. The non-terminal symbols represent abstract syntactic categories, while the terminal symbols represent the actual elements or tokens of the language.
The context-free grammar is called "context-free" because the production rules apply regardless of the context or surrounding symbols. In other words, the left-hand side non-terminal symbol can be replaced by the right-hand side sequence of symbols without considering the symbols that come before or after it. This property makes context-free grammars easier to analyze and manipulate compared to other types of grammars.
Context-free grammars are widely used in computer science and linguistics for various purposes, such as designing programming languages, parsing and analyzing natural languages, and generating valid sentences or expressions in a given language. They are also the basis for the construction of pushdown automata, which are used in the theory of computation to recognize context-free languages.