Sipser: Section 2.1
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CSC 341: Cooperative commentary | Sipser:_Chapter_2
Formal Definition of a Context-Free Grammar
From Definition 2.2 on page 104, a context-free grammar is a 4-tuple (V, Σ, R, S), where
V a finite set called the variables. Σ a finite set, disjoint from V, called the terminals. R a finite set of rules. SV is the start variable.
Formally, we can think of the rules as ordered pairs, where the first element of each rule is a variable, and the second is a string composed of variables and terminals (or possibly the empty string).
Chomsky Normal Form
Chomsky Normal Form (hereafter CNF) is a simplified form of Context Free Grammars useful for applying algorithms. Any context-free language can be generated by a CNF grammar (Theorem 2.9), so CFGs and CNF grammars are exactly equivalent.
A grammar is in CNF if every variable yields either any two variables, except the start variable, or one terminal. In addition, the start variable may yield 
. The process for converting a CFG to CNF is given on pp. 107-109.
The people behind the theory
Chomsky Normal form is (to the best of my knowledge) named for "Noam Chomsky", a preeminent linguist at MIT who, incidentally, has some fairly radical political views.
