a. Given a grammar G =(V.T.E.P) over set of alphabets = (0....9, +. . (. ) with productions . E ->I E ->E + E E ->E E E -> (E) | -> E|0|11... 19 and derive String (9+8) (6+4) b. Languages are given as, L1 = (ab" In>=0}. L2%= L(ab"), L3=D{a,ab,abb,abbb....}, L4= (X IX is over (a,b}.begins with a, followed by any number of b. Prove that L1=L2=L3=L4

a. Given a grammar G =(V.T.E.P) over set of alphabets = (0....9, +. . (. ) with productions . E ->I E ->E + E E ->E E E -> (E) | -> E|0|11... 19 and derive String (9+8) (6+4) b. Languages are given as, L1 = (ab" In>=0}. L2%= L(ab"), L3=D{a,ab,abb,abbb....}, L4= (X IX is over (a,b}.begins with a, followed by any number of b. Prove that L1=L2=L3=L4

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

See similar textbooks

Similar questions

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.
Implement a more extensive finite-state grammar for noun groups by using the examples given in Section 13.5 and test it on some NPs. Use an on-line dictionary with parts-of-speech if available; if not, build a more restricted system by hand.
Consider the language L of strings over the alphabet Σ = {a, b} which contain an equal number of a’s and b’s, and the set of b’s is consecutive in the string, e.g., ab, abba, aabb, abbbaa, aaabbbbbaa, etc. Note that ε ∈ L for completeness (0 number of a’s is equal to 0 number of b’s, which are also consecutive). Show that this language is context-free by giving a context-free grammar. Please make sure to test the answers onhttps://web.stanford.edu/class/archive/cs/cs103/cs103.1156/tools/cfg/
Consider the language L of strings over the alphabet Σ = {a, b} which contain an equal number of a's and b's, and the set of b's is consecutive in the string, e.g., ab, abba, aabb, abbbaa, aaabbbbbaa, etc. Note that ɛ € L for completeness (0 number of a's is equal to 0 number of b's, which are also consecutive). Show that this language is context-free by giving a context-free grammar.
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…
Describe an algorithm that given two context-free grammars G1 and G2 outputs YES if and only if every string generated by G1 is also generated by G2. (I.e., output YES exactly when the set of strings generated by G1 is a subset of the set of strings generated by G2.) Would such an algorithm be possible? why or why not
Formal Languages and Automata Theory Give context-free grammars that generate the following languages. In all parts, thealphabet Σ is {0,1} a. {w| w contains at least three 1s}b. {w| w starts and ends with the same symbol}c. {w| the length of w is odd}Ad. {w| the length of w is odd and its middle symbol is a 0}e. {w| w = wR, that is, w is a palindrome}f. The empty set
Consider the language L = { x ∈ [a,b]* | x starts with b, does not contain the substring aa and ends with an a} Draw the finite automata.
1) Given the alphabet as {0, 1}, write a DFA for the following three regular languages.(Give the complete description of the DFA with transition function as a table and also as a transition graph) (i) L = {w | w is a string of even length} (ii) L = {w | |w| mod 3 = 0} (iii) L = {w | w contains the string 001 as a substring} 2)Describe the extended transition function on a string recursively using transitions one symbol at a time for the three automata of the above problem. (i) A string (of length >=4) that belongs to the language (II) A string (of length >=4) that does not belong to the language
L = {(a^n)(b^m)(c^k) ; n = m or m ≠ k } Find context free grammars (with n, m, k greater than or equal to 0)
Regular grammar, S ⟶⟶ aS | bS |a | bb, will generate the following language L: Group of answer choices: A)L = L ((a +b)* (a + bbb)) b)L = L ( a(a + b)*bb) c)L = L ( (bb + a) (a + b)*) D)L = L ((a + b)* (a + bb))