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The language Balanced over E = {(,)} is defined recursively as follows 1. ЛЕ Вalanced. 2. Vx, y € Balanced, both xy and (x) are elements of Balanced. A prefix of a string x is a substring of x that occurs at the beginning of x. Prove by induction that a string x belongs to this language if and only if (iff) the statement B(x) is true. B(x): x contains equal numbers of left and right parentheses, and no prefix of x contains more right than left.

The language Balanced over E = {(,)} is defined recursively as follows 1. ЛЕ Вalanced. 2. Vx, y € Balanced, both xy and (x) are elements of Balanced. A prefix of a string x is a substring of x that occurs at the beginning of x. Prove by induction that a string x belongs to this language if and only if (iff) the statement B(x) is true. B(x): x contains equal numbers of left and right parentheses, and no prefix of x contains more right than left.

Database System Concepts
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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The language Balanced over E = {(,)} is defined recursively as follows 1. ЛЄ Вalanced. 2. Vx, y € Balanced, both xy and (x) are elements of Balanced. A prefix of a string x is a substring of x that occurs at the beginning of x. Prove by induction that a string x belongs to this language if and only if (iff) the statement B(x) is true. B(x): x contains equal numbers of left and right parentheses, and no prefix of x contains more right than left.
Transcribed Image Text:The language Balanced over E = {(,)} is defined recursively as follows 1. ЛЄ Вalanced. 2. Vx, y € Balanced, both xy and (x) are elements of Balanced. A prefix of a string x is a substring of x that occurs at the beginning of x. Prove by induction that a string x belongs to this language if and only if (iff) the statement B(x) is true. B(x): x contains equal numbers of left and right parentheses, and no prefix of x contains more right than left.
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