Alan Turing proved in 1936 that a general algorithm running on a Turing machine that solves the halting problem for all possible program-input pairs necessarily cannot exist. Hence, the halting problem is undecidable for Turing machines .
Is halting problem recursively enumerable?
The language HALT corresponding to the Halting problem is recursively enumerable , but not recursive. In particular, the universal TM accepts HALT, but no TM can decide HALT. There are languages which are not recursively enumerable, in particular the language NOTRE in the proof.
Is the halting problem unsolvable?
But the halting problem is unsolvable , which means that it is impossible to test if an arbitrary Turing machine T halts on an arbitrary input x.
Is halt undecidable?
The Halting Problem is Undecidable : Proof
Since there are no assumptions about the type of inputs we expect, the input D to a program P could itself be a program. ... Given a Pascal compiler written in Pascal, we might want to know if the compiler halts when given itself as input.
Which of the problem is 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 an undecidable problem example?
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 give example?
Example: the halting problem in computability theory
Alan Turing proved in 1936 that a general algorithm running on a Turing machine that solves the halting problem for all possible program-input pairs necessarily cannot exist. Hence, the halting problem is undecidable for Turing machines.
How do you fix halting problems?
To see this, assume that there is an algorithm PHSR (“partial halting solver recognizer”) to do that. Then it can be used to solve the halting problem, as follows: To test whether input program x halts on y, construct a program p that on input (x,y) reports true and diverges on all other inputs. Then test p with PHSR.
Can humans solve the halting problem?
Humans can’t solve the halting problem even for restricted cases where computers can, just imagine trying to analyze an otherwise trivial Turing machine that was larger than you could read in your lifetime. ... Every case a computer can solve the halting problem a human can as well, it may just take longer.
Is halting problem NP hard?
– If we had a polynomial time algorithm for the halting problem, then we could solve the satisfiability problem in polynomial time using A and X as input to the algorithm for the halting problem . – Hence the halting problem is an NP-hard problem which is not in NP . – So it is not NP-complete.
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.
What are the unsolvable problems?
An unsolvable problem is one for which no algorithm can ever be written to find the solution . 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.
Which problems are unsolvable halting problem?
One of well known unsolvable problems is the halting problem. It asks the following question: Given an arbitrary Turing machine M over alphabet = { a , b } , and an arbitrary string w over , does M halt when it is given w as an input ? It can be shown that the halting problem is not decidable, hence unsolvable.
Are undecidable statements true?
Proving a statement is true by proving it is undecidable.
What does it mean for something to be undecidable?
“Undecidable”, sometimes also used as a synonym of independent , something that can neither be proved nor disproved within a mathematical theory. ... Undecidable figure, a two-dimensional drawing of something that cannot exist in 3d, such as appeared in some of the works of M. C.
What does it mean if a problem is decidable?
(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.
