Let be a (non-empty) alphabet and let w € Σ* be a string. We say that x = Σ* is a prefix of the string w if there exists a string u = Σ* such that w = xu. Consider the following language L= {w = {a,b}*|for every prefix x ofwn(x) > na(x)} Prove that L is a context-free language. Your proof should rely on mathematical induction.

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
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Let be a (non-empty) alphabet and let w € Σ* be a string. We say that x = Σ* is a
prefix of the string w if there exists a string u = Σ* such that w = xu.
Consider the following language
L= {w = {a,b}*|for every prefix x ofwn(x) > na(x)}
Prove that L is a context-free language. Your proof should rely on mathematical induction.
Transcribed Image Text:Let be a (non-empty) alphabet and let w € Σ* be a string. We say that x = Σ* is a prefix of the string w if there exists a string u = Σ* such that w = xu. Consider the following language L= {w = {a,b}*|for every prefix x ofwn(x) > na(x)} Prove that L is a context-free language. Your proof should rely on mathematical induction.
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