Other
COS3701 Jan/Feb Supplementary Exam Paper 2023
- Course
- Institution
COS3701 Jan/Feb Supplementary Exam Paper 2023
[Show more]
Seller
Follow
StudyWellNotes
Reviews received
Content preview
UNIVERSITY EXAMINATIONSJan/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
• The mark for each question is in brackets next to the question
, COS3701
Jan/Feb 2023
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)
(b) Design a deterministic finite automaton (DFA) that will recognise all of the words in L
as defined above. (4)
(c) Use Theorem 21 to develop a context-free grammar (CFG) for the language L. (4)
(d) Convert the following CFG to Chomsky Normal Form (CNF):
S → aX Y | Y b
X → X ZY Z | 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 uv n xy n z 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}
over the alphabet Σ = {a, b} is non-context-free.
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 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 these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller StudyWellNotes. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $4.78. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
77254 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now