1. Draw the derivation tree corresponding of w = aaabbaaa using the followingcontext-free grammar%3DG = ({S), {a, b}, S, P) with productions S aSa, S bSb, S A.2. Define properly nested parenthesis structures involving two kinds of parentheses,say () and ]. (Properly nested strings are (]), ([CO1), and [0], but not (D] or (0].Define a context-free grammar for generating all properly nested parentheses.3. Show that the grammar ({S}, {a, b}, S, P) with productions S - bSaS| aSbs |A isambiguous. Draw two different parsing trees for a string that starts with b.

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1. Draw the derivation tree corresponding of w = aaabbaaa using the following context-free grammar G = ((S), {a, b}, S, P) with productions S → aSa, S → bSb, S → A. %3D 2. Define properly nested parenthesis structures involving two kinds of parentheses, say () and ]. (Properly nested strings are ([]), ([O), and [0], but not (D] or (1]. Define a context-free grammar for generating all properly nested parentheses. 3. Show that the grammar ({S}, {a, b), S, P) with productions S bSaS| aSbS |a is ambiguous. Draw two different parsing trees for a string that starts with b.

1. Draw the derivation tree corresponding of w = aaabbaaa using the following context-free grammar G = ((S), {a, b}, S, P) with productions S → aSa, S → bSb, S → A. %3D 2. Define properly nested parenthesis structures involving two kinds of parentheses, say () and ]. (Properly nested strings are ([]), ([O), and [0], but not (D] or (1]. Define a context-free grammar for generating all properly nested parentheses. 3. Show that the grammar ({S}, {a, b), S, P) with productions S bSaS| aSbS |a is ambiguous. Draw two different parsing trees for a string that starts with b.

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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In Example 6.1, show a derivation tree for the string ababbac, using both the original and the modified grammar. EXAMPLE 6.1 Consider G = ({A, B}, {a, b, c}, A, P) with productions A→a|aaA|abBc,B→abbA|b.A→a|aaA|abBc,B→abbA|b. Using the suggested substitution for the variable B, we get the grammar Ĝ with productions A→a|aaA|ababbAc|abbc,B→abbA|b.A→a|aaA|ababbAc|abbc,B→abbA|b. The new grammar Ĝ is equivalent to G. The string aaabbc has the derivation A ⇒ aaA ⇒ aaabBc ⇒ aaabbc in G, and the corresponding derivation A ⇒ aaA ⇒ aaabbc in Ĝ. Notice that, in this case, the variable B and its associated productions are still in the grammar even though they can no longer play a part in any derivation. We will next show how such unnecessary productions can be removed from a grammar.
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