(3) Let Z = {a, b}. Solve the following questions: (i) Given a regular expression r = (bb*a + aa*b)*, find an NFA to accept the language L(r). %3D (ii) Find the regular grammar for L(r) by using the above NFA.

(3) Let Z = {a, b}. Solve the following questions: (i) Given a regular expression r = (bba + aab)*, find an NFA to accept the language L(r). %3D (ii) Find the regular grammar for L(r) by using the above NFA.

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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Let G = (V, E, R, S) be a grammar with V= {S, H, Gm J}; = {h, g. j}; and the set of rules: H>h | hJG G> Gg | Sg | HgJ J→ jH | HHJ| Jj Convert this grammar to a PDA using the method we described.
2. If L is a regular language over E, what can be said about the languages L1 = E* – L and L2 = reverse(L*)? A. Li is always regular but not L2. B. L2 is always regular but not L1. C. Li and L2 are both regular. 3. What is the language generated by the grammar G: { S → aR , R → aR| baR|b }? A. (aa*b)* B. (a*b)(a*b)* C. (aa*b)(aa*b)* 4. IfL is a regular language over some alphabet E, what can be said about the language L’ = (E* – L) N reverse(L)? A. L' is surely regular. B. L’ is surely non-regular. C. Its type cannot be determined without additional information. 5. Including the trap state, how many states are there in the minimum-state DFA for the regular expression (a+b)*(b+c)* ? Also how many final states will there be in the minimum-state DFA? A. 4 states with one final state B. 3 states with two final states C. 3 states with one final state
Part B. Solve the following problems: 1. Is L = {(ab)"ba(ba)²":n 2 0} a regular language? Why? Find the grammar for it. 2. Remove the productions with forms A→ i and A→ B from the following grammar to an equivalent grammar (hint: first remove D-C; then remove C). S→ aD | aaC| CaDD D → b| Db D →C
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}
(3) Let E = {a, b}. Solve the following questions: (i) Given a regular expression r = (bb*a + aa*b)*, find an NFA to accept the language L(r). (ii) Find the regular grammar for L(7) by using the above NFA.
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.
Problem 3. Find context-free grammars for the following languages (with n ≥ 0, m≥ 0, k > 0): (a) L= {abck: n = : n = m or m≤k}. (b) L = {abck: n= m or m‡k}. (c) L = {abck, k=n+m}. (d) L= {a" bck, k = |n-m}. (e) L = {abck,k=n+2m}. (f) L = {a¹bmck, k‡n+m}.
Part B. Solve the following problems: 1. Is L = {(ab)"ba(ba)":n, m 2 0} a regular language? Why? Find the grammar for it. 2. Is L = {(ab)" ba(ba)²":n 2 0} a regular language? Why? Find the grammar for it. 3. Remove the productions with forms A→ i and A→ B from the following grammar to an equivalent grammar (hint: first remove D-C; then remove C). S → aD | aaC| CADD D→b| Db D →C
1. Consider the following context-free grammar with start symbol S, nonterminals {S, A, B, C}, and terminals {0,1}: SAO A→B A → C1 B→ 1 B→ E C→ 0 (a) Compute all the sets FIRST and FOLLOW necessary to implement a recursive decent parser for this grammar. However, do not list any unnecessary such a set. (b) Investigate all the combinations of sets FIRST and FOLLOW that are involved in the im- plementation of a recursive descent parser for this grammar. Explain how these com- bination make the grammar suitable or unsuitable (as the case might be) for recursive descent parsing.
Let ∑ = {a, b}. Solve the following questions: Given a regular expression r=bb*a+aa*b*, find an NFA to accept the language L(r). Find the regular grammar for L(r) by using the above NFA.
What can be claimed about the grammar G: {S→ alaRb, R→ b|bSa }? OA. G is a context-free grammar and L(G) is a context-free language. B. G is a context-free grammar but L(G) is actually a regular language. O C. G is a regular grammar and L(G) is a regular language. What can be said about the grammar G: {S → ORO|OR1|1RO|1R1, R → E|OR|1R }? OA. G is a context-free grammar and L(G) is a context-free language. B. G is a context-free grammar but L(G) is the regular language (0+1)²(0+1)* C. G is a regular grammar and L(G) is the regular language (0+1)(0+1)*
Given the following DFSM M, the correct statements are: S a, b a,b T □ (aa Uab Uba U bb)* is a regular expression that generates L(M). (ab Uba)* is a regular expression that generates L(M). □S → E, S → aT, S→ bT, T→ aS, T→ bS are the regular grammar rules that generate L(M). SaT, S→ bT, TaS, TbS are the regular grammar rules that generate L(M).