Context-Free Grammar

In formal language theory, a context-free grammar (CFG) is a formal grammar whose production rules can be applied to a nonterminal symbol regardless of its context. In particular, in a context-free grammar, each production rule is of the form

with $A$ a single nonterminal symbol, and $\alpha$ a string of terminals and/or nonterminals ( $\alpha$ can be empty). Regardless of which symbols surround it, the single nonterminal $A$ on the left hand side can always be replaced by $\alpha$ on the right hand side.^[1]