Logout Open In App
Open In App
Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Chapter 4: 18P (page 212)

Let C be a language. Prove that C is Turing-recognizable if a decidable language D exists such that C={x|∃yx,y∈D}.

Short Answer

Expert verified

It can be proved that that C is Turing-recognizable if a decidable language D exists such that C=x|∃yx,y∈D.

Step by step solution

01

Explain Decidable language

A language is said to be decidable if the input of a language is accepted by a Turing machine.

02

Step 2: Prove that C is Turing-recognizable

Consider that the language C is recognized by the Turing machine M and consider that an input x is given to the Turing machine.

The language D on input x,yverifies whether the y decides an accepting computation of the input string x on the machine M.

Consider, that the D is a decider.

Construct the Turing machine that decides the decidability of the C. Construct the Turing machine that searches y and find it.

The given string C=x|∃yx,y∈Dis tested using the constructed Turing machine.

If x,y∈D,the Turing machine accepts, otherwise rejects.

Therefore, it can be proved that that C is Turing-recognizable if a decidable language D exists such that C=x|∃yx,y∈D.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Say that a variable A in CFLrole="math" localid="1659808454707" G is usable if it appears in some derivation of some stringw∈G . Given a CFGG and a variable A, consider the problem of testing whetherA is usable. Formulate this problem as a language and show that it is decidable.

Question:LetINFINITEDFA={(A)|AisaDFAandLAisaninfinitelanguage}.Show thatINFINITEDFA is decidable.

Let ∑={0,1}.Show that the problem of determining whether a CFG generates some string in 1*is decidable. In other words, show that

{G|G  is  a  CFG over 0,1 and 1*∩LG≠∅}is a decidable language.

Let PALDFA={M|M is a DFA that accepts some palindrome}. Show thatPALDFAis decidable.

Prove that the class of decidable languages is not closed under homomorphism
See all solutions

Recommended explanations on Computer Science Textbooks

Fintech

Read Explanation

Problem Solving Techniques

Read Explanation

Data Representation in Computer Science

Read Explanation

Computer Systems

Read Explanation

Computer Programming

Read Explanation

Cybersecurity in Computer Science

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free