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.
What types of problems are undecidable?
There are some problems that a computer can never solve, even the world’s most powerful computer with infinite time: the undecidable problems. 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 is meant by a Decidable 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 decidable and undecidable language?
The Turing machine will halt every time and give an answer(accepted or rejected) for each and every string input. A language ‘L’ is decidable if it is a recursive language . ... If P2 was decidable, then P1 would also be decidable but that becomes a contradiction because P1 is known to be undecidable.
What is the difference between decidable and undecidable problems?
A decision problem is decidable if there exists a decision algorithm for it. Otherwise it is undecidable . To show that a decision problem is decidable it is sufficient to give an algorithm for it. On the other hand, how could we possibly establish (= prove) that some decision problem is undecidable?
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 problem how can it be solved?
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 statements true?
Proving a statement is true by proving it is undecidable.
How do you prove halting problems?
Proof: Assume to reach a contradiction that there exists a program Halt(P, I) that solves the halting problem , Halt(P, I) returns True if and only P halts on I. The given this program for the Halting Problem, we could construct the following string/code Z: Program (String x) If Halt(x, x) then Loop Forever Else Halt.
Is the halting problem decidable?
The halting problem is theoretically decidable for linear bounded automata (LBAs) or deterministic machines with finite memory . A machine with finite memory has a finite number of configurations, and thus any deterministic program on it must eventually either halt or repeat a previous configuration: ...
Is the halting problem partially decidable?
Partial Computable Problems
Example: The halting problem is partially computable . To determine HALTS(P,D), simply call P(D). Then, HALTS(P,D) halts and outputs Yes if P(D) halts, and loops otherwise. ... If a problem is not even partially computable, there is no way of checking even a YES answer.
When we say a problem is decidable give an example of undecidable problem?
Give an example of undecidable problem? algorithm that takes as input an instance of the problem and determines whether the answer to that instance is “yes” or “no”. (eg) of undecidable problems are (1) Halting problem of the TM .
What languages are not decidable?
For an undecidable language, there is no Turing Machine which accepts the language and makes a decision for every input string w (TM can make decision for some input string though). A decision problem P is called “undecidable” if the language L of all yes instances to P is not decidable.
Is the language decidable?
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.
How do you prove something is undecidable?
For a correct proof, need a convincing argument that the TM always eventually accepts or rejects any input. How can you prove a language is undecidable? To prove a language is undecidable, need to show there is no Turing Machine that can decide the language. This is hard: requires reasoning about all possible TMs.
