This problem concerns languages over the alphabet Σ = {1}. For any two integers q,r≥0, define the language Lr,q over Σ as Lr,q ={1mq+r : m ≥0}={1q,1q+r,12q+r,...}. For instance, L1,3 ={1,1111,1111111,...}. Show that for every q and r, the language Lr,q is regular.Show that if L is a regular language over Σ, then L can be written as L = Lr1,q ∪ Lr2,q ∪··∪ Lrk,q ∪ L0, where 0 ≤ r1 < ··· < rk are integers and L0 is a finite set.

To show that Lr,q is regular for every q and r, we can use the following steps:Construct a regular…

Answered: This problem concerns languages over…

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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This problem concerns languages over the alphabet Σ = {1}. For any two integers q,r

≥0, define the language Lr,q over Σ as

Lr,q ={1mq+r : m ≥0}={1q,1q+r,12q+r,...}.

For instance, L1,3 ={1,1111,1111111,...}.

Show that for every q and r, the language L_r,q is regular.
Show that if L is a regular language over Σ, then L can be written as L = Lr1,q ∪ Lr2,q ∪··∪ Lrk,q ∪ L0, where 0 ≤ r1 < ··· < rk are integers and L0 is a finite set.

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