Quantum Mechanics has formally undecidable problems. What is the philosophical significance of this?

What does it mean if 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 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.

What is an appropriate way to prove that a problem 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.

What is undecidable problem in computability?

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 is undecidable problem in automata?

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.

What are the consequences of the problem being undecidable?

What are the implications of the problem being undecidable? The problem may be solvable in some cases, but there is no algorithm that will solve the problem in all cases. A programmer develops the procedure maxPairSum() to compute the sum of subsequent pairs in a list of numbers and return the maximum sum.

What are undecidable problems discuss the Undecidability of halting problem of Turing machine?

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.

What is Decidability explain any two undecidable problems?

A decision problem P is undecidable if the language L of all yes instances to P is not decidable. An undecidable language may be partially decidable but not decidable. Suppose, if a language is not even partially decidable, then there is no Turing machine that exists for the respective language.

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.

Which among 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 the difference between undecidable problems and unreasonable time algorithms?

The difference between undecidable problems and unreasonable time algorithms is that an undecidable problem is a problem that no algorithm can be made this is always capable of providing a yes or no answer, while an unreasonable time algorithm is an algorithm with exponential efficiencies and cannot create an answer in …

What do you understand by halting problem?

In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running, or continue to run forever.

Why is the halting problem unsolvable?

unsolvable algorithmic problem is the halting problem, which states that no program can be written that can predict whether or not any other program halts after a finite number of steps. The unsolvability of the halting problem has immediate practical bearing on software development.

What is halting problem discuss the applications of halting problem of TM?

The Halting Problem is the problem of deciding or concluding based on a given arbitrary computer program and its input, whether that program will stop executing or run-in an infinite loop for the given input.