Question

Consider grammar G1. Give an equivalent CFG grammar with no unit productions, lambda productions, or useless productions. You should show the steps that you used to reach your solution.

G1:
a)S →A | B | C
b)A →aa | B
c)B →bb | C
d)C →cc | A

Answer 1

To modify grammar G1 into an equivalent CFG without lambda, unit, or useless productions, one must apply various steps like removing lambda and unit productions, as well as eliminating useless symbols, ensuring all producible strings are covered by the modified grammar.

Step-by-step explanation:

The question asks to transform grammar G1 into an equivalent context-free grammar (CFG) without unit productions, lambda productions, or useless productions. This process involves several steps to ensure that the final grammar produces all strings of the original grammar except for those that involve lambda, unit, or useless productions.

Steps to Eliminate Lambda, Unit, and Useless Productions

1. Removal of lambda productions: Introduce new non-terminals and adjust the grammar.
2. Removal of unit productions: Replace unit productions with the corresponding non-unit productions from the grammar.
3. Removal of useless productions: Identify and eliminate non-terminals that don't produce any terminal strings or those that are not reachable from the start symbol.

After applying these steps to grammar G1, we get an equivalent grammar that has no lambda, unit, or useless productions. The resulting CFG will only produce terminal strings that were also producible by the original grammar G1 minus the strings generated by lambda, unit, or useless productions.