Question

Build a Context-Free Grammar in Chomsky Normal Form that implements the following language features: (a) an integer-based data type, (b) a value-type variable declaration of an integer data type, and (c) an assignment expression that allows for two integer-based variables to be added together. Examples: (a) define an integer data type (b) int a; (c) a = 2 + 3;

Answer 1

Context Free Grammer

S->ABA
A->a|b
B->+

The conversion to Chomsky Normal Form has four main steps:

1. Get rid of all ε productions.

2. Get rid of all productions where RHS is one variable.

3. Replace every production that is too long by shorter productions.

4. Move all terminals to productions where RHS is one terminal.

Chomsky Normal Form

S0 -> AC
S -> AC
A -> a | b
B -> +
C -> BA