What is an example of an undecidable problem?

Examples – These are few important Undecidable Problems: Whether a CFG generates all the strings or not? As a CFG generates infinite strings, we can’t ever reach up to the last string and hence it is Undecidable. Since we cannot determine all the strings of any CFG, we can predict that two CFG are equal or not.

What is undecidable in Turing machine?

Undecidable Problems A problem is undecidable if there is no Turing machine which will always halt in finite amount of time to give answer as ‘yes’ or ‘no’. An undecidable problem has no algorithm to determine the answer for a given input.

What is an undecidable algorithm?

An undecidable problem is one that should give a “yes” or “no” answer, but yet no algorithm exists that can answer correctly on all inputs.

What makes a problem 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.

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.

Are undecidable problems unsolvable?

An undecidable problem is one for which no algorithm can ever be written that will always give a correct true/false decision for every input value. Undecidable problems are a subcategory of unsolvable problems that include only problems that should have a yes/no answer (such as: does my code have a bug?).

Which language is accepted by Turing machine?

The turing machine accepts all the language even though they are recursively enumerable. Recursive means repeating the same set of rules for any number of times and enumerable means a list of elements.

What are different types of Turing machine?

Variation of Turing Machine

  • Multiple track Turing Machine:
  • Two-way infinite Tape Turing Machine:
  • Multi-tape Turing Machine:
  • Multi-tape Multi-head Turing Machine:
  • Multi-dimensional Tape Turing Machine:
  • Multi-head Turing Machine:
  • Non-deterministic Turing Machine:

Are undecidable statements true?

In 1977, Paris and Harrington proved that the Paris-Harrington principle, a version of the Ramsey theorem, is undecidable in the axiomatization of arithmetic given by the Peano axioms but can be proven to be true in the larger system of second-order arithmetic.

How do you prove halting problem is undecidable?

The Halting Problem is Undecidable: Proof Proof by contradiction: Assume we have a procedure HALTS that takes as input a program P and input data D and answers yes if P halts on input D and no otherwise.