Can an undecidable problem be solved?
Undecidable means “there is no algorithm that can solve all instances and that always terminates”.
Is reducible to B and B is undecidable then?
When A is reducible to B solving A can not be “harder” than solving B. If A is reducible to B and B is decidable, then A is also decidable. If A is undecidable and reducible to B, then B is undecidable.
What does it mean when a problem is undecidable?
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 the definition of undecidable?
Definition of undecidable : not capable of being decided : not decidable … a huge popular audience, most of whom must have been baffled and exasperated by its elaborate and undecidable mystifications.—
What is an undecidable problem how is it different from a reducible problem?
The problems for which we can’t construct an algorithm that can answer the problem correctly in the infinite time are termed as Undecidable Problems in the theory of computation (TOC). A problem is undecidable if there is no Turing machine that will always halt an infinite amount of time to answer as ‘yes’ or ‘no’.
What does undecidable mean in math?
“Undecidable”, sometimes also used as a synonym of independent, something that can neither be proved nor disproved within a mathematical theory.
Why is the halting problem 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. Compilers and editors both take programs as inputs.
Why Turing machine is undecidable?
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.
Is universal Turing machine undecidable?
Mathematical theory Rice’s theorem shows that any non-trivial question about the output of a Turing machine is undecidable. A universal Turing machine can calculate any recursive function, decide any recursive language, and accept any recursively enumerable language.
Which of the following are undecidable theories?
Which among the following are undecidable theories? Explanation: Tarski and Mostowski in 1949, established that the first order theory of natural numbers with addition, multiplication, and equality is an undecidable theory.
What is meant by undecidable language?
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.