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# What is Decidability in theory of automata?

## What is Decidability in theory of automata?

A language is called Decidable or Recursive if there is a Turing machine which accepts and halts on every input string w. A decision problem P is decidable if the language L of all yes instances to P is decidable.

What is Decidability and Undecidability in TOC?

A language ‘L’ is partially decidable if ‘L’ is a RE but not REC language. Recursive language(REC) – A language ‘L’ is said to be recursive if there exists a Turing machine which will accept all the strings in ‘L’ and reject all the strings not in ‘L’. A language ‘L’ is decidable if it is a recursive language.

What do you mean by Decidability?

: capable of being decided specifically : capable of being decided as following or not following from the axioms of a logical system Was logic complete …? And was it decidable, in the sense that there was a method that demonstrated the truth or falsity of every statement? —

### What is Decidability problem?

(definition) Definition: A decision problem that can be solved by an algorithm that halts on all inputs in a finite number of steps. The associated language is called a decidable language. Also known as totally decidable problem, algorithmically solvable, recursively solvable.

What is the difference between PDA and TM?

Answer. A PDA can only access the top of its stack, whereas a TM can access any position on an infinite tape. An automaton with access to two stacks rather than just one can simulate a TM and thus has equivalent computational power.

What types of problems are undecidable?

In computability theory, an undecidable problem is a type of computational problem that requires a yes/no answer, but where there cannot possibly be any computer program that always gives the correct answer; that is, any possible program would sometimes give the wrong answer or run forever without giving any answer.

## What is difference between Decidability and Undecidability?

The problems for which we can’t construct an algorithm that can answer the problem correctly in finite time are termed as Undecidable Problems. These problems may be partially decidable but they will never be decidable.

Is CFG undecidable?

It is undecidable whether L(G)=Σ∗ for a cfg G over Σ. It is undecidable whether L(G) = R for cfg G and regular language R. 3. It is undecidable whether L(G1) ⊆ L(G2) for cfg’s G1,G2.

What is Undecidability in theory of computation?

In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is proved to be impossible to construct an algorithm that always leads to a correct yes-or-no answer.

### Are undecidable problems solvable?

The corresponding informal problem is that of deciding whether a given number is in the set. A decision problem A is called decidable or effectively solvable if A is a recursive set and undecidable otherwise.

What are the applications of TM?

Turing Machine (TM) – For understanding complexity theory. For implementation of neural networks. For implementation of Robotics Applications. For implementation of artificial intelligence.

When we say a problem is decidable?

A problem is said to be Decidable if we can always construct a corresponding algorithm that can answer the problem correctly. We can intuitively understand Decidable problems by considering a simple example. Suppose we are asked to compute all the prime numbers in the range of 1000 to 2000.