Question

2. To find a Chomsky normal form for the following grammar (10 points) STR T - aTbab R RIA first note that we don't need to add a new production S' Sto the grammar because s does not appear on the right hand side of any productions in the grammar. Next, since we have a A-production in the grammar R - A, so we use the technique in question #6 to remove the production. Afterward the grammar becomes SLT TR T aTb ab R-DRIU (2 points)

Answer 1

After removing empty production the grammar becomes:

S -> T | TR

T -> aTb | ab

R -> bR | b

After removing unit production the grammar become:

S -> aTb | ab | TR

T -> aTb | ab

R -> bR | b

For each production whose right hand side has two or more symbols we replace each terminal with new production. The grammar becomes:

S -> ATB | TR | AB

T -> ATB | AB

R -> BR | b

A -> a

B -> b

After performing the final step the CNF becomes:

S -> AU | TR | AB

T -> AU | AB

B -> BR | b

U -> TB

A -> a

B -> b