**Converting Grammar Rules to Chomsky Normal Form (CNF)**In this lesson, we will focus on converting the given set of grammar rules to Chomsky Normal Form (CNF). CNF is a type of context-free grammar where each rule is of the form:1. $ A \rightarrow BC $ (where $ A $, $ B $, and $ C $ are non-terminal symbols, and $ B $ and $ C $ are not start symbols) 2. $ A \rightarrow a $ (where $ A $ is a non-terminal symbol and $ a $ is a terminal symbol)Given grammar rules:\[ A \rightarrow ABA \ | \ B \ | \ a \ | \ ab \]\[ B \rightarrow BCB \ | \ C \ | \ b \ | \ bc \ | \ \epsilon \]\[ C \rightarrow CD \ | \ DC \ | \ c \]\[ D \rightarrow D \ | \ \epsilon \]Here are the steps involved in converting these rules to CNF:1. **Remove ε-productions**: Get rid of productions that produce an empty string (ε), except when the start symbol itself can generate ε.2. **Remove unit productions**: Productions where one non-terminal goes to another non-terminal.3. **Eliminate useless symbols**: Remove any non-terminal symbols that do not appear in any derivations of terminal strings.4. **Break down long productions**: Ensure that each production has at most two non-terminals on the right-hand side, or a single terminal.### Explanation#### Step 1: Remove ε-productions- From $ B \rightarrow \epsilon $- From $ D \rightarrow \epsilon $#### Step 2: Remove unit productionsUnit productions such as $ A \rightarrow B $, $ B \rightarrow C $, etc., need to be replaced with equivalent productions without chaining single non-terminal to another.#### Step 3: Eliminate long Productions- Productions like $A \rightarrow ABA $, $ BCB $ need to be decomposed to follow CNF rules.Here is the systematic approach to convert it to CNF:#### Intermediate Grammars Post Transformation:1. **Eliminating ε-productions:** We introduce new rules for possibilities without ε. For \( B \rightarrow b \mid C \mid bC \mid b \

Given :- A -> ABA | B | a | ab B -> BCB | C | b | bc | epsilon C -> CD | DC | c D ->…

Answered: onvert these rules to CNF. A → ABA|…

Engineering

Computer Science

onvert these rules to CNF. A → ABA| B|a|ab B→BCB|C|b|bc|e C→CD|DC|c D→D E

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

See similar textbooks

Related questions

Q: 7. Let M = ({40, 41, 42}; {a, b}, ô, qo. {42}) be the DFA with transition table: a b qo 90 91 42 |…

A: Given: M= ({qo,q1,q2}, {a,b},delta, qo, {q2} ) be the DFA with the transition table . As you have to…

Q: x)∗f(y) • f(x′) = (f(x))′′ (a) Prove f(0) = 0∗ (b) Give an example of a homomorphism from P({1,2,3})…

A: A function from Boolean algebra B to Boolean algebra B∗ is a homomorphism if it satisfies the…

Q: 7. Let M = ({90: 91; 42}, {a, b}, ô, qo; {42}) be the DFA with transition table: a | b qo 90 91 q1…

Q: 3 CNF Step 3 Perform step three of converting the following CFG’s into CNF by removing unit rules.…

A: Answer:- 3.b) S->A | epsilon A->BC B->BD B->bb C->CD C->cc D->B D->C Unit…

Q: Draw the state transition diagram for the finite automaton that models the regular expression a*bb…

A: Given regular expression is, a*bb (a + b)* Set of input alphabets= {a, b} State transition diagram…

Q: onvert the given CFG to GNF, where S -> ABA A -> aA | ε B -> bB | E

A: Context-free languages are described by context-free grammars (CFGs). A collection of recursive…

Q: Convert the following NFA (given in its transition table) to its equivalent DFA using subset…

A: GIVEN NFA: State 0 1 ->p {p.q} {p} q {r} {r} r {s} {} *s {s} {s}

Q: Eliminate useless productions from S → a |aA| B|C, A → aB|λ, B → Aa, C → cCD, D → ddd|Cd.

A: Identifying non-generating variables:

Q: Convert the following EBNF to BNF:S→A{bA}A→a[b]A

A: Given EBNF grammar is: S→A{bA}A→a[b]A S, A are the variables and a, b are terminals.

Q: Theory of Computation Assume we are given some NFA N=(QN,Σ,δN,qN,FN), produce an equivalent PDA…

A: Regular languages are accepted by NFA or DFA. Context-free languages are accepted by Pushdown…

Q: 4. Find the PDA equivalent to the given CFG with the following productions. 1. S→A, A→BC, B→ba, C→ac…

A: Context-free grammar A CFG consist of a finite group of grammar rules is a quadruple (A, B, C, G)…

Q: 5 CFG to PDA Conversion Using the technique that was covered in class, convert the following CFG to…

A: Follow this step to convert CFG to PDA 1.First push $ 2. Then put all rules of CFG on q1 3. Put…

Q: 3.b V = {S, A, B, C, D}, E = {a,b,c}, S = S, R = S →A | € A →BC B→BD | bb C→CD cc D→B|C 4 CNF Step 4…

A: Converting a Context-Free Grammar (CFG) to Chomsky Normal Form (CNF) involves transforming the CFG…

Q: Design an NFA over Σ = {a,b,c} with no more than 5 states to accept the following language: L =…

A: Answer: we have draw the NFA over ∑={a,b,c} with no more than 5 state.

Q: *I A E (a) Draw the table of distinguishabilities for this automaton. (b) Use this table to minimize…

Q: 1 CNF Step 1 Perform step one of converting the following CFG into CNF by adding a new start state…

A: A context-free grammar is in Chomsky Normal Form if every rule is of the form A→BCA→a where a is any…

Q: Q.No.10. Describe the language of the given CFG S→SS | BS | SB| USU| B→aa | bb U→ba | ab Answer Also…

Q: Q. 4 For the following DFA, find the minimal DFA (minimal number of states (Arrow represent the…

Q: Using the CYK (Cocke, Younger, Kasami) algorithm of the bbaac line, the following Chomsky Normal…

A: To test a grammar witj CNF CNF stands for Chomsky normal form A Context free Grammar is said to be…

Q: onvert the follow a) E-E+E S- OE44 |

Q: a) Let M = ({qo, q1, q2, q3, q4, qs}, {x, y, z}, qo, fs, {q3, qs}) be the Deterministic Finite…

A: Given that, set of states= {q0, q1, q2, q3, q4, q5} Set of input alphabets= {x, y, z} Initial state=…

Q: 91 €,€-$ 92 €, € > € a,ɛ→a €, € € 93 95 b,ɛ→ b,a-e €,$→€ €, E-E 94 96 c, a e W W €,$→€ 97

A: Here is the explanation related to PDA and CFG:

Q: AA S-> 0ABB A-> aBB a B-> bBB/A

A: The Given Data Construct PDA for the following CFG

Q: Convert the given CFG to CNF: S -> ABC, A -> aAb | ab, B -> bBb | b, C -> bCc | bc b. How many steps…

A: Given Grammar is: S->ABC A->aAb/ab B->bBb/b C->bCc/bc CFG to CNF S->XC X->AB…

Q: ablcd, 00 04 14 10 00 01 11 10 11 00 0 10 OO 0 1 1 oll 2014 0 Find minimited product of sum (Pos)…

A: Karnaugh Map (K-Map), Product of Sums (POS), and Canonical form are all concepts used in Boolean…

Q: a + | 90 {92} | {g1} {90} 91 {92} | {42} 93 92 {g0} | ¢ 6 | {92} 93 e NEA

A: Here in this question we have given a state table for epsilon NFA..and we have asked to Construct…

Q: Derive the Moore-type minimal flow table that specifies the same functional behaviour as the…

A: In this we use moore minimization and reduced 12 to 9 states: Explanation below:…

Q: Write the o function for the following transition graphs (1) dfa (Sp5a : Q ×£→ Q) ak a 91 92 (2) nfa…

A: Transition function for DFA is: δ:Q*ε→Q where Q= Finite set of states ε= input alphabet The…

Q: Convert these rules to CNF. A → ABA | B | a | ab B → BCB | C | b | bc | ε C → CD | DC | c D→ D |…

A: Subject: Theory of computation Convert these rules to CNF. A → ABA | B | a | ab B → BCB | C | b | bc…

Q: The contrapositive of p→q is Select one: O q→→P O q p O OP→→q None of them

A: The above question that is given above is answered below and i give proper explanation

Q: Give a PDA that generates the language L {a" bmcmb"|n, m 2 0} over E= {a,b, c}.

A: Given below is the definition of PDA and in the next step PDA diagram is shown.

Q: Convert the following CFG's to CNF. 1) S -> aX | Yb X -> S Y -> bY | b 2)…

A: 1) S -> aX | Yb X -> S Y -> bY | b Step 1: As there is start symbol S on…

Q: ct the minimum state automata for the following, 1 → A B C. C C B C

A: The Answer is in Below Steps :-

Q: for following Construct a PDA the CFG S→A

A: The Given data is Flat construct a PDA for The following CFG

Q: CFG s gi Ва

Q: 2. Convert the given CFG to CNF: S-> ASBCD | aBcD | aScD | acD | BC | CBA | BA | CA | AbCd | Abd | a…

A: The following are the steps that we use for the conversion of CFG to CNF Step 1: In…

Q: Prove that the following language is not context-free using pumping lemma: {xmy"xm| m >n + 1 > 0}…

A: Pumping Lemma for CFL states that for any Context Free Language L, it is possible to find two…

Q: Given: CFG G2 S -> ABA | C A-> Sale B-> bB | b C -> CA Clean the given CFG G2 by: 1 - Remove useless…

A: Given :

Q: Automata question Use pumping lemma to find out which of these are regular: L = {WWR | |W|=2 over…

A: Given that : Use pumping lemma to find out which of these are regular: L = {WWR | |W|=2 over…

Q: Consider the transition diagram below. What is the ε-closure of state p? → P 9 *1⁰ 00 O (p, q} O {p}…

A: Option c is correctCorrect Answer:c. {p}

Q: SHOW ALL STEPS Use K-Maps to simplify each of the following: ~x~y~z + ~xy~z + x~y~z + xy~z 2.…

A: a)~x~y~z + ~xy~z + x~y~z + xy~z

Q: Show that {wwRw | w ∈ {0, 1}* is not context free.

A: Problem is to find whether L is not context-free So K is going to be taken as context-free, P will…

Question

**Converting Grammar Rules to Chomsky Normal Form (CNF)**

In this lesson, we will focus on converting the given set of grammar rules to Chomsky Normal Form (CNF). CNF is a type of context-free grammar where each rule is of the form:

1. $ A \rightarrow BC $ (where $ A $, $ B $, and $ C $ are non-terminal symbols, and $ B $ and $ C $ are not start symbols)
2. $ A \rightarrow a $ (where $ A $ is a non-terminal symbol and $ a $ is a terminal symbol)

Given grammar rules:

\[ A \rightarrow ABA \ | \ B \ | \ a \ | \ ab \]
\[ B \rightarrow BCB \ | \ C \ | \ b \ | \ bc \ | \ \epsilon \]
\[ C \rightarrow CD \ | \ DC \ | \ c \]
\[ D \rightarrow D \ | \ \epsilon \]

Here are the steps involved in converting these rules to CNF:

1. **Remove ε-productions**: Get rid of productions that produce an empty string (ε), except when the start symbol itself can generate ε.
2. **Remove unit productions**: Productions where one non-terminal goes to another non-terminal.
3. **Eliminate useless symbols**: Remove any non-terminal symbols that do not appear in any derivations of terminal strings.
4. **Break down long productions**: Ensure that each production has at most two non-terminals on the right-hand side, or a single terminal.

### Explanation

#### Step 1: Remove ε-productions
- From $ B \rightarrow \epsilon $
- From $ D \rightarrow \epsilon $

#### Step 2: Remove unit productions

Unit productions such as $ A \rightarrow B $, $ B \rightarrow C $, etc., need to be replaced with equivalent productions without chaining single non-terminal to another.

#### Step 3: Eliminate long Productions
- Productions like $A \rightarrow ABA $, $ BCB $ need to be decomposed to follow CNF rules.

Here is the systematic approach to convert it to CNF:

#### Intermediate Grammars Post Transformation:
1. **Eliminating ε-productions:**
We introduce new rules for possibilities without ε.

For \( B \rightarrow b \mid C \mid bC \mid b \

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

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.

Similar questions

QUESTION 16: kindly minimise the given automata
Subject code cs413 Theory of computation
2. Convert the following CFGS to Chomsky Normal Form (CNF). a) E→E+E|A|F S → 0E44 | OA A → 5A7 | 2S3 | 0S4 | & F→ & | 5 (5) b) A 1|B|CA| € B→ 1BS | OSOB | & C→ x y A S→ 1A1 |OS|S|A1 c) S→ DBC | Ba B→ 0B1 | 01 | & C→ aCb | aC |Bb D→ bD|D d) S→X|Y X → Xb | Ab | & A → aAb | ab Y→ Ya | Ba| & B → bBa| ba
Simplify the following Boolean function and expression, using four-variable maps a) cF(w,x,y,z) = Σ (2,3,10,11,12,13,14,15) b) dF = x’z + w’xy’ + w(x’y + xy’) c) eF = A’B’C’D’+AC’D’+B’CD’+A’BCD+BC’D
Find a PDA for L = {x {a, b, c} *||x|a + |x|b = |x|c}.
Please help Known production as follows: E → T | EATT → F | TMFF → (E) | intA → + | -M → * | / Question: 1. Please make a Go To transisi transition diagram
Convert the following CFG into GNF. A, → A‚A, A, → A,A, I A, → A,A, | a 2.
uestion 2 Let L1 = {w | w contains any number of 1s and exactly one 0} and L2 = {w | w starts with 1 or ends with 0}. Draw the state transition diagrams for the DFAS and write the formal 5-tuple definitions for it. (. step of your construction according to the procedure specified on the text book for the regular operation union, and finally draw the state transition diagram. 2) Let L3 = L1 U L2 , design the DFA that recognizes L3, show every
Convert the following CFG to an equivalent PDA using the construction described in class. S → a Ab|bc A → aBS|aA|A B → bBc|b Give a DPDA that accepts the language {(ab)*(ba) : i > 0}
Convert the following NFA to an equivalent NFA without empty transitions. Please show the finite machine
1 1 92 93 0,1 Figure 1: A finite automaton M1 with three states a, b a a b b go 91 92 93 a Figure 2: DFA M2 for L = {w | w does not contain the substring bbb} 2. Write a regular expression for the language of the following DFA. (a) M1 (shown in Figure 1) (b) M2 (shown in Figure 2)
Construct a non- deterministic finite automaton (NFA) for below given regular expression: (0 U 1)＊ (0000000 U 111(1U0)＊111)(1 U 0)＊