**Title: Simplification of Grammar in Formal Language Theory****Objective:**To simplify the given grammar by removing useless productions, λ (epsilon) productions, and unit productions.**Grammar:**The original grammar is defined by the following production rules:- \( S \to a \mid aA \mid B \mid C \)- \( A \to aB \mid \lambda \)- \( B \to Aa \)- \( C \to cCD \)- \( D \to ddd \mid Cd \)**Task Breakdown:****(a) Remove the useless production(s).**- Identify and eliminate any productions that do not contribute to deriving any terminal strings.- Determine variables that are not reachable from the start symbol or do not lead to a terminal symbol.**(b) Remove the λ production(s).**- Eliminate productions that generate an empty string (λ-productions).- Modify the grammar to produce the same language without using any ε-productions.**(c) Remove the unit production(s). Also, remove new useless production(s) (if any).**- Identify and eliminate unit productions, which are of the form \( A \to B \).- After removing unit productions, check if any new useless productions have arisen and remove them as well.By following these steps, the grammar will be simplified while retaining its ability to produce the same language.

Answer: We need to write the how to remove the useless , λ-production and unit production so we will…

5. We want to simplify the grammar below. (a) (b) (c). S→a|aA|B|C, A → aB | X B → Aa C→CD D→ ddd | Cd Remove the useless production(s). Remove the A production(s). Remove the unit production(s). Also, remove new useless production(s)

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

See similar textbooks

Related questions

Q: emove chain rules from the following grammar. Your answer must include the CHAIN(S), CHAIN(A),…

A: Step 1: S-> A I C A -> aA | a | BB -> bB | bC->cC|c|B

Q: Consider the following grammar: S → ASB | ϵ A → aAS | a → SbS | A | bb Eliminate all…

A: We'll use a step-by-step approach to convert the provided context-free language into Chomsky Normal…

Q: 3. Consider the grammar S→ a SaaS S→ aaaS i) Is the grammar is ambiguous? ii) What is L(G) ? iii) Is…

A: Dear learner, hope you are doing well, I will try my best to answer this question. Thank You!!

Q: rite an Attribute Grammar (AG) whose base BNF is that of the following example and whose type rules…

A: Write an Attribute Grammar (AG) whose base BNF is that of the following example and whose type rules…

Q: Consider the details given below. What is the result if Arden's Rule is applied to equation 1? *…

A: Lets talk about Ardens Rule Let P and Q be two regular expressions over ∑ If P does not contain a…

Q: 3. Forma Let us consider the following Context Free Grammar G = ({S, A, B, C, D, E}, {a,b,c}, S, P)…

A: Answer

Q: Consider the following grammar and perform required tasks; S -> aA | abS A -> BB | CAC B -> bB |…

A: The Answer start from step-2.

Q: A. Construct a DFA that accepts the language generated by the grammar: SabA, ba B, BaAbb. A

A: As per our guidelines we are supposed to answer only one question. Kindly repost other questions as…

Q: Simplification of context-free grammars Eliminate all l-productions from S -> ABCd A -> BC B ->bB…

A: Given:S -> ABCdA -> BCB ->bB | λC -> λRemoving C -> λ //place λ where ever C is…

Q: 5. Obtain a grammar in Chomsky Normal Form (CNF) equivalent to the grammar G with productions, P…

A: For the given grammar we are going to convert to its equivalent CNF form. Please refer to the image…

Q: Show that the 27. Let G₁ and G₂ be two regular grammars. Show how one can derive regular grammars…

A: Grammar in theory of computation is a finite set of formal rules that are generating syntactically…

Q: 4. Consider the following context-free grammar: Goal → L L- E;L L-E E - E+T E -T T- id T- id ( ) T-…

Q: i) For the CFG G below, describe L(G): S → EaS | EE → aEb | bEa | EE | λ ii) For the CFG G below,…

A: (G):C generates strings consisting of zero or more b followed by an equal number of cs (balanced b…

Q: 1. Consider the grammar G=(V,T,E,P) with V={E,I}, T={a,b,c,+,+,(.) }. and productions E → I, E → E+…

A: i) E is starting state using production (2) E->E+E using production (3) E->E+E÷E using…

Q: Q2. Consider the following Context Free Grammar (CFG) S- Aa | BAb A BB | c B → Sd |e where {a, b, c,…

A: Parse Tree: The process of deriving a string is called as derivation. The geometrical…

Q: (3) Give a grammar G= (V,E, S̟P), where V = {4,B,C},E = {a,b},S = A, P: A→ a4|bB,B → bC | aB,C → aB…

A: According to the value given in the question, we will solve all parts.

Q: → : →int variable list →→variable list, identifier | identifier →→; ; → → identifier =

A: The programming language presented on page 7 can be rewritten as an LL1 grammar to improve its…

Q: 1. Construct a dfa that accepts the language generated by the grammar S → abA, A → baB, B → aA|bb.

A: given grammar S → abA,A → baB,B → aA|bb.

Question

**Title: Simplification of Grammar in Formal Language Theory**

**Objective:**
To simplify the given grammar by removing useless productions, λ (epsilon) productions, and unit productions.

**Grammar:**

The original grammar is defined by the following production rules:

- \( S \to a \mid aA \mid B \mid C \)
- \( A \to aB \mid \lambda \)
- \( B \to Aa \)
- \( C \to cCD \)
- \( D \to ddd \mid Cd \)

**Task Breakdown:**

**(a) Remove the useless production(s).**

- Identify and eliminate any productions that do not contribute to deriving any terminal strings.
- Determine variables that are not reachable from the start symbol or do not lead to a terminal symbol.

**(b) Remove the λ production(s).**

- Eliminate productions that generate an empty string (λ-productions).
- Modify the grammar to produce the same language without using any ε-productions.

**(c) Remove the unit production(s). Also, remove new useless production(s) (if any).**

- Identify and eliminate unit productions, which are of the form \( A \to B \).
- After removing unit productions, check if any new useless productions have arisen and remove them as well.

By following these steps, the grammar will be simplified while retaining its ability to produce the same language.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

.. Convert the following Context Free Grammar (CFG) into an equivalent Push Down Automata (PDA) (note that in this problem, the start symbol is C'): C → AC A|E E → OG1|1G0 G → AGA|A|e A → 0|1
Do ONLY: 1, 2, 3, 6, 7, 11. == Page 102 (You are asked to find regular grammar in questions 2, 6, 7, 11. To do so, find the NFA first, then each edge in the NFA gives a production in the regular grammar).
1. Consider the CFG below.Give parse trees and derivations for each string.a. ab. a+ac. a+a+a d. ((a))
Consider the grammar G = ({S, A}, S, {a, b}, P) with the following set of production rules P: S → aS|baA|abaAA → aAbb|aAb|ε 1. Determine what the language generated by G is. You may only use set builder notation and/or language operators in your answer. A proof is not required. 2. Show that the grammar G is ambiguous by: (a) Providing two distinct leftmost derivations for the same string w ∈ L(G).(b) Providing two distinct parse trees for the same string w ∈ L(G).
Transform the grammar into Chomsky Normal Form: S → AB | aB A → aab|λ B→ bbA Transform the grammars into CNF: a) SaSb|bSa|a|b b) S→ asblab c) Sab|as|aas d) S → ABb|a, A → aaA|B, B → bAb
(5) Consider the grammar G=(V,T,E,P) with V={E,I}, T={a, b, c, +,-, *, (. )}, and productions R → R+R|R -R | R* | (R) I = a|b|c. ) Show that G is ambiguous by giving two different derivation trees for string b+c-a (ii) Change the above grammar into the one without ambiguity.
(a) Consider the following context free grammars (CFG): i. ii. B> dBb | bBd | dCb C>aC |E E>FG F> fgFg | fgGg |f G→ g Do left factoring of the above grammars (if necessary). Why is it needed to do left factoring of a grammar? Explain with proper example. (b) Write down the regular expression and draw the transition diagram of how a lexical analyzer will detect all the positive or negative floating point numbers (eg. 1.5, 45, 2. , - 98. , – 6.71,- .39 etc.). 2.
Upvote is guaranteed for correct and detailed answer. Thank you!
SOLVE ONLY: 3, 6, 7, 11
Can I get the answer for number 5?