Discussion
Let Σ = {a, b}, Γ = {a, b, c} and define 'h' by :
h(a) = ab
h(b) = bbc
Then h(aba) = abbbcab
The homomorphic image of L = {aa, aba} is the language .............. .
Answer: A
The image is h(L) = {abab, abbbcab}.
A homomorphism replaces each symbol by its image string, and the image of a language is the set of images of its strings:
\[ \begin{aligned} h(aa) &= h(a)\,h(a) = ab\,ab = abab \\ h(aba) &= ab\,bbc\,ab = abbbcab \end{aligned} \]
L has only two strings, so h(L) has at most two. The strings aaaa and bbbb in options B and C are not images of anything in L, and option D's strings do not match h(a) = ab and h(b) = bbc.
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development