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Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN: 9780133594140
Author: James Kurose, Keith Ross
Publisher: PEARSON
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
Transcribed Image Text:**Exercise: Context-Free Grammar (CFG) for Natural Language**
**Objective:**
Define a Context-Free Grammar (CFG) for Natural Language to demonstrate that the following sentences would have very similar derivations and therefore can be well-formed:
1. A beautiful girl sings.
2. A green idea dances.
**Discussion:**
The task requires defining the rules of a CFG that generate the given sentences. A well-formed CFG allows the decomposition of sentences into their grammatical components, ensuring that similar structures share derivational processes.
**Example Sentences:**
- A beautiful girl sings.
- A green idea dances.
**Steps to Define CFG:**
1. Identify the components of the sentences:
- Determiner (Det): "A"
- Adjective (Adj): "beautiful", "green"
- Noun (N): "girl", "idea"
- Verb (V): "sings", "dances"
2. Define the production rules:
Here, S represents a sentence, NP denotes a noun phrase, and VP stands for a verb phrase.
```
S → NP VP
NP → Det Adj N
VP → V
Det → 'A'
Adj → 'beautiful' | 'green'
N → 'girl' | 'idea'
V → 'sings' | 'dances'
```
**Explanation:**
According to the production rules:
- *S* (Sentence) is broken down into *NP* (Noun Phrase) and *VP* (Verb Phrase).
- *NP* is further broken down into *Det* (Determiner), *Adj* (Adjective), and *N* (Noun).
- *VP* for the given sentences only contains a *V* (Verb).
- The terminals ('A', 'beautiful', 'green', 'girl', 'idea', 'sings', 'dances') are the actual words in the sentences.
**Derivation for "A beautiful girl sings":**
1. S
2. NP VP
3. Det Adj N VP
4. 'A' Adj N VP
5. 'A' 'beautiful' N VP
6. 'A' 'beautiful' 'girl' VP
7. 'A' 'beautiful' 'girl' V
8. 'A' 'beautiful' 'girl' 'sings'
**Derivation for "A green idea dances":**
1.
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- Consider the language over the alphabet Σ = {0, 1} containing strings which include nonempty binaries(strings with 0’s and 1’s) that start with 1 and end with 0 and have at least three digits. For example, 110and 1100 are such binaries, while 10 and 010 are not.1. Write a regular expression for this language 2. Draw a DFA diagram for this language, with no more than six states. 3. Is the language regular? Why or why not?arrow_forwardQuestion 4. Consider the language L over the alphabet (a, b, c, d } such that L = {abcd":n> 0, m>0}. Develop a CFG for the language L. Show the production sequence to derive two different valid strings of length 5arrow_forwardSolve 12aarrow_forward
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