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COS2601 Assignment 4 marked memo 2024
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UNISA 2024 COS2601-24-Y Assessments Assessment 4QUIZ
Started on Wednesday, 11 September 2024, 10:06 PM
State Finished
Completed on Sunday, 15 September 2024, 8:22 PM
Time taken 3 days 22 hours
Grade 19.00 out of 20.00 (95%)
,Question 1
Correct
Mark 1.00 out of 1.00
Consider the following FA with the regular expression r:
By applying Kleene’s theorem, an FA must be built for the regular expression r*. In the process a transition table is compiled.
We compile a suitable transition table by using the algorithm provided in Cohen page 129.
1. From the discussion, it is clear that this option is the correct
New state Read an a Read an b
option
±z1 = w1 z2 z3
z2 = w1 z2 z3
z3 = w2 z2 +z4
+z4 = w1 or w3 +z4 +z5
+z5 = w1 or w2 or w3 +z4 +z5
2.
New state Read an a Read an b
z1 = w1 z1 z2
z2 = w2 z1 +z3
+z3 = w1 or w3 +z3 +z4
+z4 = w1 or w2 or w3 +z3 +z4
3.
New state Read an a Read an b
±z1 = w1 ±z1 z2
z2 = w2 ±z1 +z3
+z3 = w1 or w3 +z3 +z4
+z4 = w1 or w2 or w3 +z3 +z4
4.
New state Read an a Read an b
z1 = w1 z1 z2
z2 = w2 z1 +z3
+z3 = w3 +z3 +z3
Your answer is correct.
By applying Kleene’s theorem, an FA must be built for the regular expression r*. In the process, a transition table is compiled.
Which one of the following represents the correct transition table?
In state ±z1 = x1 we can read
, an a: we go to +x2 or (because +x2 is a final state) to x1; so we have x1 or +x2 = +z3 which is also a final state; or
a b: we go to x3 = z4.
In state z2 = x1 we can read
an a: we go to +x2 or (because +x2 is a final state) to x1; so we have x1 or +x2 = +z3 which is also a final state; or
a b: we go to x3 = z4.
In state z3 = x1 or +x2 we can read
an a: if in x1, we go to +x2 or (because +x2 is a final state) to x1; if in x2, we stay in +x2 or (because +x2 is a final state) to x1;
so together we have x1 or +x2 which is +z3; or
a b: if in x1, we go to x3; if in x2, we also go to x3; so together we have x3, which is z4.
In state z4 = x3 we can read
an a: we go to +x2 or (because +x2 is a final state) to x1; so together we have x1 or +x2 which is +z3; or
a b: we stay in x3, which is z4.
We provide the compiled table:
New state Read an a Read an b
±z1 = w1 z2 z3
z2 = w1 z2 z3
z3 = w2 z2 +z4
+z4 = w1 or w3 +z4 +z5
+z5 = w1 or w2 or w3 +z4 +z5
The correct answers are:
New state Read an a Read an b
±z1 = w1 z2 z3
z2 = w1 z2 z3
z3 = w2 z2 +z4
+z4 +z5
+z4 = w1 or w3
+z4 +z5
+z5 = w1 or w2 or w3
,
New state Read an a Read an b
z1 z2
z1 = w1
z1 +z3
z2 = w2
+z3 = w3 +z3 +z3
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