Downloaded by palmer kamulee (kamuleepalmer@gmail.com)
, lOMoAR cPSD| 47715245
COS3701
Jan/Feb 2023
UNIVERSITY EXAMINATIONS
Jan/Feb 2023
COS3701
Theoretical Computer Science III
80 Marks
Duration 2 Hours
Welcome to the COS3701 exam.
Examiner name: Ms DR Mokwana
Internal moderator name: Prof F Bankole
This paper consists of 5 pages.
Instructions:
• Upload you answer script in a single PDF file format not password
protected
• No emailed scripts will be marked
• Preview your submission to ensure legibility and correct script file
has been uploaded
• Students who have not utilised IRIS invigilation app will be
subjected to disciplinary process
• Students suspected of dishonesty conduct during examination will
be subjected to disciplinary process
• Write neatly and legibly
Downloaded by palmer kamulee (kamuleepalmer@gmail.com)
, lOMoAR cPSD| 47715245
COS3701
Jan/Feb 2023
• The mark for each question is in brackets next to the question
Question 1 [16]
(a) Determine a regular expression for the language L over the alphabet
{a, b} that consists of all words that have at least one b but contain
exactly one aa substring (and no other as).
Example of words in the language are aab, bbbaabbb,
bbbbaabbbbbbbb etc.
Examples of words that are not in the language are a, aba, bbab,
aaabbbb, baabbbbaabb
etc. (2)
Design a deterministic finite automaton (DFA) that will recognise all
(b)
of the words in L
as defined above. (4)
Downloaded by palmer kamulee (kamuleepalmer@gmail.com)
, lOMoAR cPSD| 47715245
COS3701
Jan/Feb 2023
(c) Use Theorem 21 to develop a context-free grammar (CFG) for (4)
the language L.
(d) Convert the following CFG to Chomsky Normal Form
(CNF):
S → aX Y | Y b
X→XZYZ|
a Y → bY |
Λ
Z→a|Λ (6)
Question 2 [10]
Build a deterministic pushdown automata (DPDA) that
accepts the language
L = {(ab)n(aa)m(ba)n−1 | n ≥ 1, m ≥ 1} over the alphabet Σ =
{a, b}.
Question 3 [12]
The pumping lemma with length for context-free languages (CFLs) can
be stated as follows: Let L be a CFL generated by a CFG in CNF with p
live productions. Then any word w in L with length > 2p can be broken
into five parts:
w = uvxyz such that length(vxy) ≤ 2p length(x) > 0 length(v) +
length(y) > 0 and such that all the words uvnxynz with n ∈ {2, 3,
4, . . .} are also in the language L.
Use the pumping lemma with length to prove that the language
L = {(a)n(b)2n+2(a)n−1 | n ≥ 1}
Downloaded by palmer kamulee (kamuleepalmer@gmail.com)
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through EFT, credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying this summary from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller Seller28. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy this summary for R46,79. You're not tied to anything after your purchase.