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If L is a regular language, prove that Lı = {uv : u E L, \v| = 2} is also regular. %3D

If L is a regular language, prove that Lı = {uv : u E L, \v| = 2} is also regular. %3D

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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Use the construction in Theorem 4.1 to find nfa's that accept (a) L((ab)*a*)n L(baa*) (b) L(ab*a*) N L(a*b*a) The nor of two languages is nor(L1, L2) = {w : w ¢ L1 and w ¢ L2} Show that the faily of regular language is closed under the nor operation. Define the complementary or (cor) of two languages by cor (L1, L2) w: w Πσως Τ? Show that the faily of regular language is closed under the cor operation. Suppose we know that L1 U L2 is regular and that Lı is finite. Can we conclude from this that L2 is regular? If L is a regular language, prove that Lı = {uv : u E L, Jv| = 2} is also regular. If L is a regular language, prove that the language {uv : u € L, v E I
Transcribed Image Text:Use the construction in Theorem 4.1 to find nfa's that accept (a) L((ab)*a*)n L(baa*) (b) L(ab*a*) N L(a*b*a) The nor of two languages is nor(L1, L2) = {w : w ¢ L1 and w ¢ L2} Show that the faily of regular language is closed under the nor operation. Define the complementary or (cor) of two languages by cor (L1, L2) w: w Πσως Τ? Show that the faily of regular language is closed under the cor operation. Suppose we know that L1 U L2 is regular and that Lı is finite. Can we conclude from this that L2 is regular? If L is a regular language, prove that Lı = {uv : u E L, Jv| = 2} is also regular. If L is a regular language, prove that the language {uv : u € L, v E I
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