5 The production rules for a grammar G with start symbol S, terminals a, b, and c and non-terminals X, Y, and Z is given below: S + XY X + a|YZ Y + b|ZX z - cjXY G: a) Show that G generates bacab (i.e., that s bacab). b) Is G a regular grammar? Explain. c) Is G a type 2 (context free) grammar? Explain. 6 Show that if A is a regular language, then the complement of A is also regular. (We can denote the complement of A as A- A = {r |z ¢ A}.)

5 The production rules for a grammar G with start symbol S, terminals a, b, and c and non-terminals X, Y, and Z is given below: S + XY X + a|YZ Y + b|ZX z - cjXY G: a) Show that G generates bacab (i.e., that s bacab). b) Is G a regular grammar? Explain. c) Is G a type 2 (context free) grammar? Explain. 6 Show that if A is a regular language, then the complement of A is also regular. (We can denote the complement of A as A- A = {r |z ¢ A}.)

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:S →aAbB | CCA →a | CB | εB →bB | dC →aC | d | ε where S, A, B, and C are non-terminals, S is the start variable, and a, b, c, and d are terminals. Does the grammar have a predictive recursive descent parser? If the grammar has a predictive recursive descent parser, show that the conditions of predictive parsing apply for every non-terminal. On the other hand, if the grammar does not have a predictive recursive descent parser, then show ALL the conditions of predictive parsing that fail.
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.
Complete the proof of Theorem 6.4. Theorem 6.4: Let G = (V, T, S, P) be any context-free grammar without λ-productions. Then there exists a context-free grammar bG = (bV , b T, S, b P) that does not have any unit-productions and that is equivalent to G. 1
Question 3 a) Consider the grammar E → E + E | E ∗ E | (E) | id. I. Change ambiguous grammar to non-ambiguous? II. Give a context-free grammar for generating the set of palindromes over the alphabet a,b. III. Give a context-free grammar for generating all strings over a,b such that | a |= 2∗ | b
Consider the grammar G = ({S, A}, S, {a, b}, P) with the following set of production rules P: S → aS|baA|abaAA → aAbb|aAb|ε 1. Determine what the language generated by G is. You may only use set builder notation and/or language operators in your answer. A proof is not required. 2. Show that the grammar G is ambiguous by: (a) Providing two distinct leftmost derivations for the same string w ∈ L(G).(b) Providing two distinct parse trees for the same string w ∈ L(G).
(20 Points) Consider the following grammars where S is the start symbol and a, b, and c are terminal symbols and A, B, and C are non-terminal symbols.S ---> aA | bB | cCA --> aA | aB | aB --> bB | bC | bC --> cC | cExplain in your own words what the grammar generates. Which of the following sentences are in the language generated by the grammar? Show derivations. If a sentence cannot be generated by the grammar, explain why abcabcab aaaaaabb cccccaaaa bbbbbbbc aaaaaaccc
Show a derivation tree for w = aaabbaaa using the grammar in Example 5.1. EXAMPLE 5.1 The grammar G = ({S}, {a, b}, S, P), with productions S→aSa,S→bSb,S→λ,S→aSa,S→bSb,S→λ, is context-free. A typical derivation in this grammar is S ⇒ aSa ⇒ aaSaa ⇒ aabSbaa ⇒ aabbaa. This, and similar derivations, make it clear that L (G) = {wwR : w ∈ {a, b}*}.
QUESTION 4 : Consider G be a Context Free Grammar for which the production Rules are given below:S -> aB|bAA -> a|aS|bAAB -> b|bS|aBBDrive the string aaabbabbba using the above grammar by using Left Most Derivation.
Exercise 1 Consider the following BNF grammar for a language. Answer the questions below according to the grammar. <fun> -> <pon> <fun> -> <pon> + <fun> <ybu> -> <fun> <ybu> -> <fun> @ <ybu> <pon> -> A <pon> -> Y <pon> -> B <pon> -> U A. What is the associativity of the @ operator: left-right-neither B. What is the associativity of the + operator: left-right-neither C. Which operator has higher precedence: @-+-neither D. The grammar is left recursive-right recursive-both-neither
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…
Question 13) Consider the following context-free grammar G over the alphabet Σ = {a, b, c}, where S is thestart variable:S → aSb | ε | acSbaUsing the rules of the grammar G, give a derivation for the word acabba.
Let G = (V, T, S, P ) be a phrase-structure grammar with V = { 0, 1, A, S }, T = { 0, 1 } and the set of productions P consisting of S →1 1S, S →2 00A, A →3 0A, A →4 0. A. Show whether 111000 ∈ L(G). B. Show whether 11001 ∈ L(G).