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COS3701 Assignment 3 memo 2024

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  • Course
  • Theoretical Computer Science III (COS3701)
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  • University Of South Africa (Unisa)

COS3701 Assignment 3 memo 2024: Material to be tested: Cohen, Chapter 19, 21 - 25 Question 1 [10] Build/design a Turing machine (TM) that determines whether a given word contains at least one insta...

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  • August 28, 2024
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  • 2024/2025
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  • University of South Africa (Unisa)
  • Theoretical Computer Science III (COS3701)
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COS3701 Assignment 3 memo 2024
Detailed complete explanation and everything that is needed


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, Question 1 Build/design a Turing machine (TM) that determines whether
a given word contains at least one instance of the substring aab. If it
does, then the TM should write a T on the tape after the input word

Explanation:
This TM checks whether a given word contains the substring "aab". If the substring is found, it
writes "T" on the tape after the input word.
• States and Transitions: The TM starts in an initial state, it start with either an "a" or "b". It
reads the input symbols one by one, looking for the sequence "aab". If it finds "a", it stays in
the current state; when it sees another "a", it might move to a new state. Upon seeing "b"
after two "a"s, it transitions to a state where it will write "T" after the word.
• Halting: The TM halts once it has written "T" on the tape, signaling that the substring was
found.




Question 2 Build/design a TM that:

· accepts all words that start with an a, and ends with a b,

· loops forever on all words that start with a b, and

· rejects all other words.

Explanation:
This TM accepts words that start with an "a" and end with a "b". It loops forever on words that start
with a "b" and rejects all other words.
• States and Transitions: For words starting with "a" and ending with "b", the TM transitions
through states that validate the sequence. If it encounters an invalid pattern, it either loops
(in case of starting with "b") or moves to a reject state.
• Looping: For words starting with "b", it keeps the TM in a loop without ever reaching a
halting state.

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