Introduction to Context-Free Grammar
As we know that grammar is a set of rules, similarly context-free grammar has some set of recursive rules through which a pattern is generated. Which describes context-free languages. This Grammar is called context-free grammar because in this production rules are independent of context.
The productions in regular grammar are restricted in two ways: The left side must be a single variable, while the right side has a special form. To create grammars that are more powerful, we must relax some of these restrictions. By retaining the restriction on the left side, but permitting anything on the right, we get context-free grammar.
Definition of Context-free grammar
In general, a context-free grammar G is defined as a quadruple(4-tuple) of (V, Σ(T), R(P), S) with a production rule S→a where,
V is a set of variables,
Σ set of terminal symbols and subset of V,
R is a set of rules called as production rules (V − Σ) × V*,
S is a start symbol V − Σ.
(Nonterminals are usually represented by capital letters and terminals by lower case letters.)
Every CFG production rule can be written as S→a, where S is a unique nonterminal symbol and a is some combination of non-terminals or production rules.
For example, the following is context-free grammar, as is any combination of the rules in isolation.
Rule 1: S→aSa
Rule 2: S→bSb
Rule 3: S→ϵ
(Epsilon is the empty string.)
In other words, we can say that context-free grammar is a model of a language. It consists of several rules. A rule defines the replacement of a symbol with another symbol. In order to generate a sentence from the language, you are allowed to apply one rule at a time. A rule does not depend on the context (hence the context freeness).
The following are examples of strings that may be constructed by this grammar: that is, members of the CFL, L, described by this CFG, and the corresponding derivations.
aa: Rule 1, followed by Rule 3
aabb: Rule 1, followed by Rule 2, followed by Rule 3.
The empty string (Rule 3)
Grammar G, with productions
S → abB,
A → aaBb,
B → bbAa,
A → λ,
is context-free. We leave it to the reader to show that
L (G) = {ab (b b a a) n b b a (b a) n : n ≥ 0}
Context-free grammars are used in compilers and in particular for parsing, taking a string-based program, and figuring out what it means. Typically, CFGs are used to define the high-level structure of a programming language.
What are the applications of context-free grammar?
- Context-free grammar is used as a specification mechanism for programming languages
- Context-free grammar is used as the basis for compiler design and implementation.
- Designers of compilers use such grammars to implement the compiler’s components, such as scanners, parsers, code generators, and code synthesizers.
- The implementation of almost any programming language is preceded by a context-free grammar that specifies it.
Context-free grammar is to describe context-free language. Context-free grammar is a set of recursive rules used to generate patterns of strings. Context-free grammar can describe all regular languages and more, but it cannot describe all possible languages. Context-free grammar is studied in the fields of theoretical computer science, compiler design, and linguistics. CFGs are used to describe programming language parsers programs in compilers that can be generated automatically from context-free grammar.
