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1. Give a context-free grammar generating the following language (Σ= {a, b, #}): {w#x | the reverse of w is a substring of x for w, x = {a, b}*} 2. Give a context-free grammar that generates the following language! k≥ 2, each x; Є {a, b}*, and for X1 some i and ji, x₁ = x R (= {a, b, #} and x denotes the reverse of xj.) 3. Give a pushdown automaton recognizing the following language: {w the length of w is odd and the middle symbol is a 0} (Σ= {0,1}) 4. Prove the following language is context-free: {x#y | x, y = {a, b}* and x y} (Σ= {a, b, #}) MacBook Air

1. Give a context-free grammar generating the following language (Σ= {a, b, #}): {w#x | the reverse of w is a substring of x for w, x = {a, b}*} 2. Give a context-free grammar that generates the following language! k≥ 2, each x; Є {a, b}*, and for X1 some i and ji, x₁ = x R (= {a, b, #} and x denotes the reverse of xj.) 3. Give a pushdown automaton recognizing the following language: {w the length of w is odd and the middle symbol is a 0} (Σ= {0,1}) 4. Prove the following language is context-free: {x#y | x, y = {a, b}* and x y} (Σ= {a, b, #}) MacBook Air

Database System Concepts
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
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1. Give a context-free grammar generating the following language (Σ= {a, b, #}): {w#x | the reverse of w is a substring of x for w, x = {a, b}*} 2. Give a context-free grammar that generates the following language! k≥ 2, each x; Є {a, b}*, and for X1 some i and ji, x₁ = x R (= {a, b, #} and x denotes the reverse of xj.) 3. Give a pushdown automaton recognizing the following language: {w the length of w is odd and the middle symbol is a 0} (Σ= {0,1}) 4. Prove the following language is context-free: {x#y | x, y = {a, b}* and x y} (Σ= {a, b, #}) MacBook Air
Transcribed Image Text:1. Give a context-free grammar generating the following language (Σ= {a, b, #}): {w#x | the reverse of w is a substring of x for w, x = {a, b}*} 2. Give a context-free grammar that generates the following language! k≥ 2, each x; Є {a, b}*, and for X1 some i and ji, x₁ = x R (= {a, b, #} and x denotes the reverse of xj.) 3. Give a pushdown automaton recognizing the following language: {w the length of w is odd and the middle symbol is a 0} (Σ= {0,1}) 4. Prove the following language is context-free: {x#y | x, y = {a, b}* and x y} (Σ= {a, b, #}) MacBook Air
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