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DFA Questions

The document outlines various tasks related to constructing Deterministic Finite Automata (DFA) for different languages over specified alphabets. It includes requirements for strings based on their starting and ending characters, specific substrings, and conditions like even counts of characters or divisibility by numbers. Additionally, it specifies the design of DFAs for various properties such as length constraints and divisibility tests.

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58 views1 page

DFA Questions

The document outlines various tasks related to constructing Deterministic Finite Automata (DFA) for different languages over specified alphabets. It includes requirements for strings based on their starting and ending characters, specific substrings, and conditions like even counts of characters or divisibility by numbers. Additionally, it specifies the design of DFAs for various properties such as length constraints and divisibility tests.

Uploaded by

tej.17893
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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DFA questions

1. Construct a DFA that accepts


1. All strings Σ{0,1} that start with 0.
2. All strings Σ{0,1} that end with 1.
3. All strings Σ{0,1} of length exactly 2.
4. All strings Σ{a,b} but that should not contain ‘aabb’ in it.
5. All strings Σ{a,b} that contain a in it.
6. All strings Σ{a,b} such that it should start with a and end with b.
7. All strings Σ{a,b} such that it should not start with a and end with b.
8. All strings Σ{a,b} such that it should either start with a or end with b.
9. All strings Σ{a,b} such that it should neither start with a nor end with b.
10. Only those binary numbers that has even numbers of 1’s Σ{0,1}.
11. All strings Σ{0,1} such that it has ‘101’ as a substring in it.
12. All strings Σ{0,1} beginning with ‘101’ substring.
13. All strings Σ{a,b} that :
a. contains substring ‘abb’
b. end with substring ‘abb’
14. All strings Σ{0,1} such that it contains substring ‘11’ but does not contain substring
‘00’.
15. All strings Σ{a,b} ending in ‘ab’ or ‘ba’.
16. All strings Σ{a,b} containing both ‘ab’ and ‘ba’ as a substring.
17. All strings Σ{a,b} that end up in ‘aa’ or ‘bb’.
18. All strings Σ{0,1} where second symbol is 0 and fourth symbol is 1.

2. Design DFA for L(m) = {w ∈ {a,b} | w contains odd number of a’s}


3. Design DFA for L(m) = {a,b} for no of a’s & no of b’s are even.
4. Design DFA for language of all strings of length atmost 4 Σ{a,b}
5. Design DFA for language of all binary strings divisible by 3.
6. Design DFA for language of all decimal numbers divisible by 3.
7. Design DFA for divisibility by 5 tester over decimal alphabets.

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