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 forX1some i and ji, x₁ = xR(= {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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Answered: 1. Give a context-free grammar…

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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3.
Prove that each of the following languages is context-free by constructing a context-free grammar (CFG) that generates that language. The notation num, (c) means the number of times character c appears in string w; the notation w means the reverse of string w. L = {a¹b³ck | i, j, k € N and i ‡ j or i
For each of these languages, give both a context-free grammar and a push down automaton. Briefly explain how your CFG and PDA work. Your CFG should be relatively simple and contain at most 6 variables. For this question, your PDA cannot be directly convertedfrom your CFG (a)L1={ x#y | x is a prefix of yR, and y∈{a,b}* } ,Σ ={a,b,#} Recall that wR is w written backwards, and u is a prefix of v if v=ut for some stringt.For example bb#abb is in L1, but a#ab is not. (b)L2={ aibjck | i ≥ j or j ≥ k } (c)L3 = {w∈{a,b}* | w contains an unequal number of a’s and b’s}
2. Give a context-free grammar that generates the following language: {x1#*#. |k≥ 2, each xi € {a, b}*, and for` some i and j #i, x₁ = x² #22#...#k
This question is about context-free grammars and parsing, and Turing machines (TM’s). Question 1) Consider the following context-free grammar G over the alphabet Σ = {a, b, c}: S → aSb | ε | acSba | abc Using any of the grammar transformation techniques we saw in this module, construct a CNFgrammar that generates the same language as the grammar G of Question 1.Make sure you include in your answer all individual steps that you followed. Please help me with this question :)
Give a context-free grammar to generate each of the following languages: (a) {0 110 | mn, and m,n > 2} (b) {u v w v² | u, v, w € {a,b}* and lul = lwl = 2}
Give a context-free grammar for the following languages: R a. L₁ = {a" ww²b"; w € *, n bª; w € Σ*, n ≥ 0} ; Σ = {a,b} b. L₂ = {anbmck; n = morm ≤k; n, m, k ≥ 0}; E = {a,b,c} {a¹
Consider a grammar for expressions is defined as follows:<assign> → <id> = <expr><id> → A | B | C | D<expr> → <id> + <expr>| <id> * <expr>| ( <expr> )| <id>Give a recursive descent algorithm for the BNF defined above.You may abstract away some details and are expected to make your answer using pseudo code.
Consider the following language. L = {w E {0, 1}* : w contains one more 1 than Os} Your friend comes up with the following context-free grammar for L. S → A1A A → 01A | 10A | 0A1 | 1A0 Unfortunately, her grammar is wrong! Find a string w E Lthat can not be derived in your friend's grammar.
Assumptions ... Alphabet = {a, b} • L1 = { a"b" : n ≥ 0 ^ n mod 3 = 0} L2 = {anbm : n ≥ 0 ^ m ≥ 0 ^ n = m −1} To do in this exercise ... ⚫ Find a context-free grammar G such that L(G) = L1 L2, the concatenation of languages L1 and L2. ⚫ Save your context-free grammar as a JFLAP.jff file, and submit that .jff file to Canvas as your solution to th is exercise.
Give a context-free grammar that generates the following language, with alphabetΣ is {0, 1, #}: {x1#x2# . . . #xk | k ≥ 1, each xi € {0, 1} *, and for some i and j, xi = x R j }
Give a context-free grammar that generates the following language, with alphabetΣ is {0, 1, #}: {x1#x2# . . . #xk | k ≥ 1, each xi E {0, 1} *, and for some i and j, xi = x R j }

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