Automata Theory Questions Medium
A context-free grammar (CFG) is a formal grammar that consists of a set of production rules used to generate strings in a formal language. It is a type of formal grammar where each production rule has a single non-terminal symbol on the left-hand side and a sequence of terminals and/or non-terminals on the right-hand side.
In a CFG, the non-terminal symbols represent variables that can be replaced by a sequence of terminals and/or non-terminals, while the terminal symbols represent the basic elements or symbols of the language. The production rules define how these symbols can be combined to form valid strings in the language.
The CFG is called "context-free" because the replacement of a non-terminal symbol with its corresponding right-hand side can occur without considering the context or surrounding symbols. This means that the replacement of a non-terminal symbol is solely based on the non-terminal symbol itself, rather than its position within a string.
Context-free grammars are widely used in computer science, particularly in the field of formal language theory and compiler design. They are used to describe the syntax of programming languages, define the structure of programming constructs, and generate parse trees for syntactic analysis.