COS3701 Assignment 3 (COMPLETE ANSWERS) 2025

COS3701
Assignment 3
(COMPLETE
ANSWERS) 2025
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COS3701 Assignment 3 (COMPLETE
ANSWERS) 2025
Course

 Theoretical Computer Science III (COS3701)
 Institution
 University Of South Africa (Unisa)
 Book
 Theoretical Computer Science

COS3701 Assignment 3 (COMPLETE ANSWERS) 2025 - DUE 2025; 100%
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Question 1 [10] Given that L1 = (aa)* and L2 = (a + b)*ab(a + b)*. Find
grammars for L1 and L2. Then use Theorem 37 to find L1L2.



✅ Step 1: Define grammars for L1 and L2



Language L1 = (aa)*

This means the strings consist of zero or more repetitions of “aa”. So valid strings are: ε, aa,
aaaa, aaaaaa, etc.

We define grammar G1 = (V1, Σ, R1, S1) where:

 V1 = {S1}
 Σ = {a}
 R1:
o S1 → aaS1 | ε

✔ This generates zero or more "aa" substrings.



Language L2 = (a + b)ab(a + b)