Problem 3. (Regular Expressions-DFA) Show that the following languages are regular by giving a regular expression and DFA that describes each one: a) L1= {all strings over Σ= {0, 1} containing at least three 1's}. b) L2= {all strings over Σ= {0, 1} that contain the substring 11 and the substring 00}. c) L3= {all strings over Σ= {0, 1} that does not contain the substring 111}. d) L4= {all strings over Σ = {a,b,c} with length less than 2}. e) L5= {all strings over Σ= {a,b,c} in which the number of c's is divisible by 32).

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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Problem 3. (Regular Expressions-DFA) Show that the following languages are regular by giving a
regular expression and DFA that describes each one:
a) L1= {all strings over Σ= {0, 1} containing at least three 1's}.
b) L2= {all strings over Σ =
c) L3 = {all strings over Σ =
d) L4= {all strings over Σ =
e) L5= {all strings over Σ =
{0, 1} that contain the substring 11 and the substring 00}.
{0,1} that does not contain the substring 111}.
{a,b,c} with length less than 2}.
{a,b,c} in which the number of c's is divisible by 32}.
Transcribed Image Text:Problem 3. (Regular Expressions-DFA) Show that the following languages are regular by giving a regular expression and DFA that describes each one: a) L1= {all strings over Σ= {0, 1} containing at least three 1's}. b) L2= {all strings over Σ = c) L3 = {all strings over Σ = d) L4= {all strings over Σ = e) L5= {all strings over Σ = {0, 1} that contain the substring 11 and the substring 00}. {0,1} that does not contain the substring 111}. {a,b,c} with length less than 2}. {a,b,c} in which the number of c's is divisible by 32}.
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