(3) Give a grammarG= (V,E, S̟P), where V = {4,B,C},E = {a,b},S = A, P: A→ a4|bB,B → bC | aB.C → aB | aC | 2.(a) Is Ga regular grammar? Why?(b) Find an nfa which accepts the language L(G).(c) Find the regular expression r associated with the language accepted by the above nfa.(d) Find regular language L(7) from the above r.

In this question, we are given a grammar and we have to check whether this grammar is regular…

Answered: (3) Give a grammar G= (V,E, S̟P), where…

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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Consider the grammar G = (V, T, E, P) with V = {E, I}, T = {a, b, c, +, *, (, ) }, and productionsE⟶⟶ I |E + E |E * E |(E) I ⟶⟶ a | b | cThe grammar is _________. Group of answer choices: A)ambiguous B)unambiguous
Consider the following two grammars. (a) 1 start --> E$ 2. E --> ( E plus E 3. E ---.> num (b) 1. Start --> E $ 2. E ---> E ( plus E 3. E --> num which of these grammars, if any, is ambiguous? prove your answer by showing two distinct derivations of same input string for the ambiguous grammar(s).
What is meant by ambiguous CFG? Prove that the grammar E→E+E/E *E /a is ambiguous.
The quotient of two languages L_1/L_2 = { x | ∃y ∈ L_2 (xy ∈ L_1) } That is, the set of strings from which a string in L_1 could be created by appending a string in L_2. So, {aaa, aab, aba, abb} / {a, bb} = {aa, ab, a} Are regular languages closed with respect to quotient? What if L_1 is not regular but L_2 is? Is L_1/L_2 guaranteed to be regular? What if L_2 is not regular but L_1 is? Is L_1/L_2 guaranteed to be regular? Exhibit a nonregular language L1 and regular language L2 for which L1/L2 is nonregular.
1)Let G = (V, ∑, R, S) be a grammar with V = {S, H, Gm J}; ∑ = {h, g, j}; and the set of rules: S → H H → h | hJG G → Gg | Sg | HgJ J → jH | HHJ| Jj a)Convert this grammar to a PDA using the method we described. b)Convert G to Chomsky normal form.
answer the following and explain Establish that L is context-free by building a CF grammar for L = {0n1m: n does not equal 4m and n,m ≥0}
explain in depth and give answer Establish that L is context-free by building a CF grammar for L = {0n1m: 3m ≤ n ≤ 4m and m ≥ 0}.
Consider the grammar G below in the input alphabet {x, y, z, *}, with leading non-terminal S' in rule 1. S'→S $ S → E * F S → F E → x E → z F y F F → E a) Build the LR(1) automaton of grammar G. Is this grammar LR(1)? b) List the LR(1) items in the last automaton state reached (without performing reductions on the last character) when the input is: x* z zx zxy For this question, indicate the lookahead and the top of the stack, it is also necessary to list the states in the same order as the grammar rules. Also, list the lookaheads in the order {?, $, x, y, z, *} c) Check if G is LALR. If so, answer with the number of states eliminated in relation to the previous automaton. If not, answer with -1
Grammar and its application to FractalsLet G=(N,T,P,∑) where ∑ is the start symbol, N = {D}, T = {d, r, l}, andP = {∑→D, D→DrDllDrD, D → d} 1. Give the most specific type of grammar G.2. Show the leftmost derivation sequence of the string drdlldrd, (i.e. When deriving a new sentential form, always replace one Nonterminal at a time and always replace the leftmost Nonterminal)3. Suppose d is an abstraction of a command to draw a straight line of fixed length in the current direction, r is an abstraction of a command to turn right by 60 degrees, and l is an abstraction of a command to turn left by 60 degrees. Assuming that you are to start from a point and that the starting direction is to proceed horizontally to the right, show the figure represented by the generated string drdlldrd.4. The string drdlldrdrdrdlldrdlldrdlldrdrdrdlldrd can also be generated. Assuming that you are to start from a point and that the starting direction is to proceed horizontally to the right, show the figure…
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}
In each case below, given the context-free grammar G, find a CFG G1 inChomsky normal form generating L(G) − {lamda}.a. G has productions S → SS | (S) | Lamdab. G has productions S → S(S) | Lamdac. G has productionsS → AaA | CA | BaB A → aaBa | CDA | aa | DCB → bB | bAB | bb | aS C → Ca | bC | D D → bD | Lamda
Let LL be the set of (codes for) context-free grammars GG such that L(G)L(G) contains at least one palindrome. Show that LL is undecidable. Hint: Reduce PCP to LL by constructing, from each instance of PCP a grammar whose language contains a palindrome if and only if the PCP instance has a solution

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