Context free grammar (part-1/2) - Theory of computation
In Theory of computation, How to write context free grammar(CFG) is explained with suitable examples. Regular languages(RL) are the subset of Context free languages. So for every RL, CFG can be written.
Context-free grammars (CFGs) are used to describe context-free languages. A context-free grammar is a set of recursive rules used to generate patterns of strings. A context-free grammar can describe all regular languages and more, but they cannot describe all possible languages.
Context-free grammars are studied in fields of theoretical computer science, compiler design, and linguistics. CFG’s are used to describe programming languages and parser programs in compilers can be generated automatically from context-free grammars.
Context Free Grammars
Context-free grammars can generate context-free languages. Context-free grammars are named as such because any of the production rules in the grammar can be applied regardless of context—it does not depend on any other symbols that may or may not be around a given symbol that is having a rule applied to it.
Context-free grammars have the following four components:
A context-free grammar can be described by a four-element tuple (V, \Sigma, R, S),(V,Σ,R,S), where
V is a finite set of variables (which are non-terminal,usually written in Uppercase)
Σ is a finite set ((disjoint from V)V) of terminal symbols(usually written in Lowercase)
R is a set of production rules where each production rule maps a variable to a string w, w∈(V∪Σ)∗
S (which is in V)is a start symbol.
Context-free grammars (CFGs) are used to describe context-free languages. A context-free grammar is a set of recursive rules used to generate patterns of strings. A context-free grammar can describe all regular languages and more, but they cannot describe all possible languages.
Context-free grammars are studied in fields of theoretical computer science, compiler design, and linguistics. CFG’s are used to describe programming languages and parser programs in compilers can be generated automatically from context-free grammars.
Context Free Grammars
Context-free grammars can generate context-free languages. Context-free grammars are named as such because any of the production rules in the grammar can be applied regardless of context—it does not depend on any other symbols that may or may not be around a given symbol that is having a rule applied to it.
Context-free grammars have the following four components:
A context-free grammar can be described by a four-element tuple (V, \Sigma, R, S),(V,Σ,R,S), where
V is a finite set of variables (which are non-terminal,usually written in Uppercase)
Σ is a finite set ((disjoint from V)V) of terminal symbols(usually written in Lowercase)
R is a set of production rules where each production rule maps a variable to a string w, w∈(V∪Σ)∗
S (which is in V)is a start symbol.
Related links:
Chomsky Hierarchy of formal languages in Automata theory
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