COS3701 Assignment 2 (COMPLETE ANSWERS) 2025 - DUE 2025; 100% TRUSTED Complete, trusted solutions and explanations. Ensure your success with us..

COS3701
Assignment 2
(COMPLETE
ANSWERS) 2025
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, Exam (elaborations)
COS3701 Assignment 2 (COMPLETE
ANSWERS) 2025
Course

 Theoretical Computer Science III (COS3701)
 Institution
 University Of South Africa (Unisa)
 Book
 Theoretical Computer Science

COS3701 Assignment 2 (COMPLETE ANSWERS) 2025 - DUE 2025; 100%
TRUSTED Complete, trusted solutions and explanations. Ensure your success
with us..



Question 1 10 Find CFGs for all words that do not have the substring aba
over the alphabet Σ = {a b}.

To define a Context-Free Grammar (CFG) that generates all words over the alphabet Σ = {a,
b} that do NOT contain the substring "aba", we need to carefully avoid introducing this
specific sequence.



✅ Step-by-step plan:

We define a grammar that ensures “aba” never appears. We do this by keeping track of what
has come so far — especially if an "a" has appeared and might be followed by "b", which might
then be followed by "a" (and thus form “aba”).



✅ Variables (non-terminals):

Let’s define the states (non-terminals) as follows:

 S: Start symbol, represents strings that have not yet started forming "aba".
 A: Represents strings that have just seen an "a".
 AB: Represents strings that have just seen "ab" — we must not allow another "a" after
this.