First, find the binary equivalent of the position in English Alphabet of the letter D in , in 5 bits.
For example, if the letter is 'B', the position is 2, so the binary equivalent is '00010'. If it is A, it will be '00001'.
Now, check if that string belongs to the language of the following grammar, using CYK algorithm. You have to show the steps.(S is the start symbol)
S --> AB
A --> BC | 0
B --> AC | 1
C --> CB | 0
Answers & Comments
Answer:
Let's first find the binary equivalent for the letter 'D'. In the English alphabet, 'D' is the 4th letter. We'll represent its position in 5 bits:
Position of 'D' = 4
Binary equivalent of 4 in 5 bits = 00100
Now, we have the binary string '00100'. We will use the CYK algorithm to check if it belongs to the given grammar. The CYK algorithm works by constructing a parsing table and filling it based on the production rules.
Grammar:
1. S --> AB
2. A --> BC | 0
3. B --> AC | 1
4. C --> CB | 0
Let's build the CYK parsing table step by step.
1. Initialize a 5x5 table:
```
| 1 | 2 | 3 | 4 | 5 |
1 | | | | | |
2 | | | | | |
3 | | | | | |
4 | | | | | |
5 | | | | | |
```
2. Fill in the diagonal with the corresponding terminal symbols (the characters of the binary string).
```
| 1 | 2 | 3 | 4 | 5 |
1 | 0 | | | | |
2 | | 0 | | | |
3 | | | 1 | | |
4 | | | | 0 | |
5 | | | | | 0 |
```
3. Use the grammar rules to fill in the other cells based on the production rules:
- S --> AB: Check if S derives A and B.
```
| 1 | 2 | 3 | 4 | 5 |
1 | 0 | | | | S |
2 | | 0 | | A | |
3 | | | 1 | | |
4 | | | | 0 | |
5 | | | | | 0 |
```
- A --> BC: Check if A derives B and C.
```
| 1 | 2 | 3 | 4 | 5 |
1 | 0 | | | | S |
2 | | 0 | A | A | |
3 | | | 1 | | |
4 | | | | 0 | |
5 | | | | | 0 |
```
- B --> AC: Check if B derives A and C.
```
| 1 | 2 | 3 | 4 | 5 |
1 | 0 | | | | S |
2 | | 0 | A | A | B |
3 | | | 1 | | |
4 | | | | 0 | |
5 | | | | | 0 |
```
- C --> CB: Check if C derives C and B.
```
| 1 | 2 | 3 | 4 | 5 |
1 | 0 | | | | S |
2 | | 0 | A | A | B |
3 | | | 1 | C | |
4 | | | | 0 | |
5 | | | | | 0 |
```
The final table shows that the string '00100' can be generated by the grammar, and it belongs to the language described by the grammar. The top-right cell contains 'S', indicating that the entire string can be derived from the start symbol 'S' using the given grammar.
Explanation:
it would be really helpful if you would mark my answer as the brainliest