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Convert the CFG G4 given in Exercise 2.1 to an equivalent

Introduction to the Theory of Computation | 3rd Edition | ISBN: 9781133187790 | Authors: Michael Sipser ISBN: 9781133187790 221

Solution for problem 2.11 Chapter 2

Introduction to the Theory of Computation | 3rd Edition

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Introduction to the Theory of Computation | 3rd Edition | ISBN: 9781133187790 | Authors: Michael Sipser

Introduction to the Theory of Computation | 3rd Edition

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Problem 2.11

Convert the CFG G4 given in Exercise 2.1 to an equivalent PDA, using the procedure given in Theorem 2.20.

Step-by-Step Solution:

2.11 Convert the CFG  given in Exercise 2.1 to an equivalent PDA, using the procedure given in Theorem 2.20.

Theorem 2.20

A language is context free if and only if some pushdown automaton recognizes it.

Step By Step Solution

Step 1 of 2

Given, CFG ,

                        

                        

                        

The formal details of the construction of the pushdown automaton . To make the construction clearer, we use shorthand notation for the transition function. This notation provides a way to write an entire string on the stack in one step of the machine. We can simulate this action by introducing additional states to write the string one symbol at a time.

The following is an informal description of P :

  1. Place the marker symbol  and the start variable on the stack.
  2. Repeat the following steps forever.
  1. If the top of stack is a variable symbol, nondeterministically select one of the rules for the variable and substitute the variable by the string on the right-hand side of the rule.
  2. If the top of stack is a terminal symbol, read the next symbol from the input and compare it to the symbol. If they match, repeat. If they do not match, reject this branch of nondeterminism.
  3. If the top of stack is the symbol , enter the accept state. Doing so accepts the input if it has all been read.


Step 2 of 2

Chapter 2, Problem 2.11 is Solved
Textbook: Introduction to the Theory of Computation
Edition: 3
Author: Michael Sipser
ISBN: 9781133187790

The answer to “Convert the CFG G4 given in Exercise 2.1 to an equivalent PDA, using the procedure given in Theorem 2.20.” is broken down into a number of easy to follow steps, and 19 words. Since the solution to 2.11 from 2 chapter was answered, more than 1352 students have viewed the full step-by-step answer. This full solution covers the following key subjects: . This expansive textbook survival guide covers 11 chapters, and 401 solutions. This textbook survival guide was created for the textbook: Introduction to the Theory of Computation, edition: 3. Introduction to the Theory of Computation was written by and is associated to the ISBN: 9781133187790. The full step-by-step solution to problem: 2.11 from chapter: 2 was answered by , our top Science solution expert on 01/05/18, 06:19PM.

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Convert the CFG G4 given in Exercise 2.1 to an equivalent