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What is an undecidable set?
Undecidable problem in computer science and mathematical logic, a decision problem that no algorithm can decide, formalized as an undecidable language or undecidable set. “Undecidable”, sometimes also used as a synonym of independent, something that can neither be proved nor disproved within a mathematical theory.
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 are undecidable languages?
(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.
What is an undecidable problem computer science?
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 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 problems are decidable?
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.
Can a language be decidable and undecidable?
yes instances to P is not decidable or a language is undecidable if it is not decidable. If a language is not even partially decidable , then there exists no Turing machine for that language.
Are undecidable languages infinite?
Only infinite languages can be undecidable. To be undecidable, there must be individual strings in the language that cause the TM to fail. Indeed, there must be infinitely many such strings (otherwise, the poorly behaved ones could be handled by special-case logic).
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.
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?
Are there any uncountably many undecidable problems?
There are uncountably many undecidable problems, so the list below is necessarily incomplete. Though undecidable languages are not recursive languages, they may be subsets of Turing recognizable languages: i.e., such undecidable languages may be recursively enumerable.
Which is an example of an undecidable problem in mathematics?
Many, if not most, undecidable problems in mathematics can be posed as word problems: determining when two distinct strings of symbols (encoding some mathematical concept or object) represent the same object or not. For undecidability in axiomatic mathematics, see List of statements undecidable in ZFC . Hilbert’s Entscheidungsproblem.
Which is an example of a semi decidable problem?
Semi-Decidable problems are those for which a Turing machine halts on the input accepted by it but it can either halt or loop forever on the input which is rejected by the Turing Machine. Such problems are termed as Turing Recognisable problems. Examples – We will now consider few important Decidable problems:
Can a undecidable language be a recursive language?
Though undecidable languages are not recursive languages, they may be subsets of Turing recognizable languages: i.e., such undecidable languages may be recursively enumerable.