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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.
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 are undecidable problems discuss the Undecidability of halting problem of Turing machine?
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.
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 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.
When problem is a undecidable in TOC?
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’.
Is undecidable a real word?
Undecidable definition (mathematics, computing theory) Incapable of being algorithmically decided in finite time. For example, a set of strings is undecidable if it is impossible to program a computer (even one with infinite memory) to determine whether or not specified strings are included.
What is an undecidable proposition?
In foundations of mathematics: Recursive definitions. … formal mathematical system will contain undecidable propositions—propositions which can be neither proved nor disproved.
Which of the following is are undecidable?
Which of the following is/are undecidable? Explanation: First is Emptiness for CFG; whether a CFG is empty or not, this problem is decidable. Second is everything for CFG; whether a CFG will generate all possible strings (completeness of CFG), this problem is undecidable.
When a problem is said to be undecidable give an example?
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 does undecidable mean in mathematics?
What is an undecidable Turing machine?
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. Examples.
Which problem is undecidable Mcq?
Undecidability MCQ Question 2 Detailed Solution According to Rice’s theorem, emptiness problem of Turing machine is undecidable.
Which one 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 halting problem of Turing machine?
The halting problem is a decision problem about properties of computer programs on a fixed Turing-complete model of computation, i.e., all programs that can be written in some given programming language that is general enough to be equivalent to a Turing machine.
Which of the following are undecidable theories?
What does it mean if a language is undecidable?
(definition) Definition: A language for which the membership cannot be decided by an algorithm — equivalently, cannot be recognized by a Turing machine that halts for all inputs.