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Show that the PDA constructed in Example 7.6 (attached file) accepts the strings aabb and aaabbbb, and that both strings are in the language generated by the given grammar.

Show that the PDA constructed in Example 7.6 (attached file) accepts the strings aabb and aaabbbb, and that both strings are in the language generated by the given grammar.

Computer Networking: A Top-Down Approach (7th Edition)
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...
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Show that the PDA constructed in Example 7.6 (attached file) accepts the strings aabb and aaabbbb, and that both strings are in the language generated by the given grammar.

Example 7.6: Construct a pda to accept the language generated by grammar with productions S → aSbb | a. First, we transform this grammar into Greibach Normal Form: S → aSA | a A → bB B → b We define the pda to have three states – an initial state qo, a final state q2, and an intermediate state q1. We define the initial transition rule to push the start symbol S on the stack: 8(%0; A, z) = {(41, S2)} We simulate the production S → aSA with a transition that reads a from the input and replaces S on the top of the stack by SA. Similarly, we simulate the production S → a with a transition that reads a while simply removing S from the top of the stack. We represent these two productions in the pda as the nondeterministic transition rule: 8(41, a, S) = {(41, SA), (41, A) } Doing the same for the other productions, we get transition rules: 8(q1, b, A) = {(q1, B)} 8(q1, b, B) = {(1, X)} When the stack start symbol appears at the top of the stack, the derivation is complete. We define a transition rule to move the pda into its final state: 8(41, A, z) = {(42, A)}
Transcribed Image Text:Example 7.6: Construct a pda to accept the language generated by grammar with productions S → aSbb | a. First, we transform this grammar into Greibach Normal Form: S → aSA | a A → bB B → b We define the pda to have three states – an initial state qo, a final state q2, and an intermediate state q1. We define the initial transition rule to push the start symbol S on the stack: 8(%0; A, z) = {(41, S2)} We simulate the production S → aSA with a transition that reads a from the input and replaces S on the top of the stack by SA. Similarly, we simulate the production S → a with a transition that reads a while simply removing S from the top of the stack. We represent these two productions in the pda as the nondeterministic transition rule: 8(41, a, S) = {(41, SA), (41, A) } Doing the same for the other productions, we get transition rules: 8(q1, b, A) = {(q1, B)} 8(q1, b, B) = {(1, X)} When the stack start symbol appears at the top of the stack, the derivation is complete. We define a transition rule to move the pda into its final state: 8(41, A, z) = {(42, A)}
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