Chapter 1: Q44P (page 90)

Let B and C be languages over $\sum = \{0, 1\} .$ Define
$B \neg C = {w^I B | f o r s o m e y^I C, s t r i n g s w a n d y c o n t a i n e q u a l n u m b e r s o f 1 s}$
Show that the class of regular languages is closed under the $\overset{1}{\leftarrow}$ operation.

Short Answer

Expert verified

The class of regular languages closed under $B \leftarrow C$ operation.

Step by step solution

To explain regular languages

B and C are the two languages and

$B \leftarrow C = {w \in B | f o r s o m e y \in C, s t r i n g s w a n d y c o n t a i n e q u a l n u m b e r s o f 1 s}$ over the alphabet.

So, it is given that B and C are regular languages

To Recognizes the language

Let $M_{B}$ be the DFA that recognizes the language B

$M_{B} = (Q_{B}, \sum, δ_{B}, q_{B}, F_{B})$

Let $M_{c}$ be the DFA that recognizes the language C

$M_{C} = (Q_{C}, \sum, δ_{C}, q_{C}, F_{C})$

To construct an NFA which recognizes $B \leftarrow C$ .

Construction of NFA to recognize $B \leftarrow C$ .

Let $N = (Q, \sum, δ, q, F)$ be the NFA.

Therefore, class of regular languages closed under $B \leftarrow C$ operation.

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Let B and C be languages over $\sum = \{0, 1\} .$ Define
$B \neg C = {w^I B | f o r s o m e y^I C, s t r i n g s w a n d y c o n t a i n e q u a l n u m b e r s o f 1 s}$
Show that the class of regular languages is closed under the $\overset{1}{\leftarrow}$ operation.

Short Answer

Step by step solution

To explain regular languages

To Recognizes the language

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Let B and C be languages over ∑=0,1. DefineB¬C={w^IB| for some y^IC, strings w and y contain equal numbers of 1s}Show that the class of regular languages is closed under the←1operation.

Short Answer

Step by step solution

To explain regular languages

To Recognizes the language

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Computer Science Textbooks

Problem Solving Techniques

Computer Organisation and Architecture

Computer Network

Computer Programming

Algorithms in Computer Science

Data Structures

Study anywhere. Anytime. Across all devices.

Let B and C be languages over $\sum = \{0, 1\} .$ Define
$B \neg C = {w^I B | f o r s o m e y^I C, s t r i n g s w a n d y c o n t a i n e q u a l n u m b e r s o f 1 s}$
Show that the class of regular languages is closed under the $\overset{1}{\leftarrow}$ operation.