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Chapter 0: Q23P (page 1)

Let itB be any language over the alphabet 鈭�. Prove that B=B+iffBB鈯�B

Short Answer

Expert verified

Thus, the solution isx1,x2,x3鈭�B .

Step by step solution

01

Introduction

鈥楤鈥� is apply to any language over that alphabet鈭�.

To be confirmation about formula :-

B=B+iff BB鈯�B

02

Explanation

One Direction: -


Assume: - B=B+ ----------- result (1)

To Show : -BB鈯�B

Since, forevery language BB鈯�B+ ------- result (2)

By Sabstitating (1) and (2) , it can be obtained that BB鈯�B. Hence, it鈥檚 been confirmed that BB鈯�B iff role="math" localid="1663234619808" BB=B+

Other Direction : -

Assume : - BB鈯�B

To sure and confirmed : - -BB=B+

It鈥檚 in knowledge in every or any language BB鈯�B+ --------- (3)

Let w be a string of elements, such that w鈭�B+w鈭�B.

If w鈭�B+than W the string can be divided within elements. x1,x2,x3,.....xksuchasw=x1,x2,x3....xkFor x1鈭�Bandk猢�1 .

After long duration x1x2鈭�Band it is assumed that BB鈭�B.

Same way, it hold for the different elements x3, as well as x3鈭�Band BB鈯�B.Thus

x1,x2,x3鈭�B .

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Most popular questions from this chapter

Write a formal description of the following graph.

Show that for any language A , a language B exists,whereA鈮�TandB'TA. .

Read the informal definition of the finite state transducer given in Exercise 1.24. Give the state diagram of an FST with the following behaviour. Its input and output alphabets are 0,1 . Its output string is identical to the input string on the even positions but inverted on the odd positions. For example, on input 0000111 it should output 1010010 .

Show that if G is a CFG in Chomsky normal form, then for any stringw鈭�L(G) of lengthn猢�1, exactly2n-1 steps are required for any derivation of w.

Give an example of an undecidable language B, where B鈮�mB.
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