Final answer:
To transform the given grammar into Chomsky normal form, follow steps like removing epsilon-productions, eliminating unit productions, converting long productions into shorter ones, and removing terminals that appear alone. The resulting grammar will be in Chomsky normal form.
Step-by-step explanation:
To transform the given grammar into Chomsky normal form, we need to follow certain steps. First, we need to remove ε-productions. Then, we need to eliminate unit productions. Next, we convert long productions into shorter ones by introducing new variables. Finally, we remove any terminals that appear alone in a production.
In the given grammar, we start by removing ε-productions, which are productions that have ε (empty string) on the right-hand side: S → ab XYX. Next, we remove the unit productions, which are productions that have only one variable on the right-hand side: S → ab XYX, X → b X a, Y → YX a, Y → X
After removing the unit productions, we have the following grammar: S → ab XYX, X → b X a, Y → YX a, Y → X. To eliminate long productions, we introduce new variables and rewrite the grammar as follows: S → ab XZ, X → b X a, Z → YX, Y → YX a, Y → X. Now, we remove the terminals that appear alone in a production: S → AB XZ, X → B X A, Z → YX, Y → YX A, Y → X. The resulting grammar is in Chomsky normal form.