Chapter 4: Q3E (page 193)

Let $A L L_{DFA} = {<A> | A is a DFA and L (A) = \sum *}$ . Show that $A L L_{DFA}$ is decidable.

Short Answer

Expert verified

It can be shown that $A L L_{DFA}$ is decidable.

Step by step solution

Explain decidability

The automata and the grammars helps decide the outcome of the undecidable problems. The Deterministic Finite Automata determines the state of the string given as input.

Show that ALLDFA is decidable

Consider the given context-free language, $A L L_{DFA} = \{<A> | A is a DFA that recognizes \sum *\}$ . Assume that the following Turing Machine $M$ decides $A L L_{DFA}$ .

$M ='' On input <A> where A is a DFA:$

Construct $D F A E$ recognizes the complete situation, the start state $A$ , until new states are marked by the transition, if no accept state is marked “accept”, otherwise, “reject”.
Run the Turing Machine $T$ , on input $<B>$ , where $T$ decides $E_{DFA}$ .
If $T$ accepts, “accept”.
If $T$ rejects, “reject”.

Therefore, the $A L L_{DFA}$ is decidable.

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!

Recommended explanations on Computer Science Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Let $A L L_{DFA} = {<A> | A is a DFA and L (A) = \sum *}$ . Show that $A L L_{DFA}$ is decidable.

Short Answer

Step by step solution

Explain decidability

Show that ALLDFA is decidable

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Computer Science Textbooks

Databases

Big Data

Game Design in Computer Science

Data Structures

Functional Programming

Issues in Computer Science

Study anywhere. Anytime. Across all devices.

Let ALLDFA={A|A is a DFA andLA=∑*}. Show thatALLDFAis decidable.

Short Answer

Step by step solution

Explain decidability

Show that ALLDFA is decidable

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Computer Science Textbooks

Databases

Big Data

Game Design in Computer Science

Data Structures

Functional Programming

Issues in Computer Science

Study anywhere. Anytime. Across all devices.

Let $A L L_{DFA} = {<A> | A is a DFA and L (A) = \sum *}$ . Show that $A L L_{DFA}$ is decidable.