Give context-free grammars that generate the following languages. In all parts the alphabet Σ is {0, 1}. a) {w € Σ* | w contains at least two Os} b) {w € Σ* | the length of w is even} c) {w ¤ Σ* | w starts and ends with the same symbol} d) {w € Σ* | the length of w is odd and its middle symbol is a 1} e) The empty set f) The empty string

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
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Give pushdown automata for the languages in question 1.
Note: Some of these languages are regular (every regular language is also a context-free
language). Therefore, you will not need a stack for recognizing them. That is, a finite
automaton will suffice for recognizing each of these languages.
Transcribed Image Text:Give pushdown automata for the languages in question 1. Note: Some of these languages are regular (every regular language is also a context-free language). Therefore, you will not need a stack for recognizing them. That is, a finite automaton will suffice for recognizing each of these languages.
Give context-free grammars that generate the following languages. In all parts the alphabet
Σ is {0, 1}.
a) {w € Σ* | w contains at least two Os}
b) {w € * | the length of w is even}
c) {w ¤ Σ* | w starts and ends with the same symbol}
d) {w € Σ* | the length of w is odd and its middle symbol is a 1}
e) The empty set
f) The empty string
Transcribed Image Text:Give context-free grammars that generate the following languages. In all parts the alphabet Σ is {0, 1}. a) {w € Σ* | w contains at least two Os} b) {w € * | the length of w is even} c) {w ¤ Σ* | w starts and ends with the same symbol} d) {w € Σ* | the length of w is odd and its middle symbol is a 1} e) The empty set f) The empty string
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