Question

In: Computer Science

Ex#3: Give a string of lengths, 4, 6, 8 generated by the following grammar G =...

Ex#3: Give a string of lengths, 4, 6, 8 generated by the following grammar G = (V, T, S. P).
S → 0S
S --> 0S1S
S --> λ

Solutions

Expert Solution

Answer:

String length String
4 0000
6 000000
8 00000000

Explanation:

Given production rules.

S → 0S
S --> 0S1S
S --> λ

String derivation:

4 lenght string: 0000

Step1: S → 0S

Step2: substitute 0S in S, S → 00S , [Since S --> 0S]

Step3: substitute 0S in S, S → 000S , [Since S --> 0S]

Step4: substitute 0S in S, S → 0000S , [Since S --> 0S]

Step5: substitute λ in S, S → 0000 , [Since S --> λ, which is null string]

So we can derive 0000 as 4 length string from the given rules.

6 lenght string: 000000

Step1: S → 0S

Step2: substitute 0S in S, S → 00S , [Since S --> 0S]

Step3: substitute 0S in S, S → 000S , [Since S --> 0S]

Step4: substitute 0S in S, S → 0000S , [Since S --> 0S]

  Step5: substitute 0S in S, S → 00000S , [Since S --> 0S]

  Step6: substitute 0S in S, S → 000000S , [Since S --> 0S]

Step7: substitute λ in S, S → 000000 , [Since S --> λ, which is null string]

So we can derive 000000 as 6 length string from the given rules.

8 lenght string: 000000

Step1: S → 0S

Step2: substitute 0S in S, S → 00S , [Since S --> 0S]

Step3: substitute 0S in S, S → 000S , [Since S --> 0S]

Step4: substitute 0S in S, S → 0000S , [Since S --> 0S]

  Step5: substitute 0S in S, S → 00000S , [Since S --> 0S]

  Step6: substitute 0S in S, S → 000000S , [Since S --> 0S]

  Step7: substitute 0S in S, S → 0000000S , [Since S --> 0S]

  Step8: substitute 0S in S, S → 00000000S , [Since S --> 0S]

Step9: substitute λ in S, S → 00000000 , [Since S --> λ, which is null string]

So we can derive 00000000 as 8 length string from the given rules.
***Please give Upvote ***

venereology answered 2 years ago
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