How do you show that a function is Turing computable?

According to this question, the definition of a computable function is: If f:Σ∗→Σ∗ is function, and ∃ a Turing machine which on the input w∈Σ∗ writes f(w), ∀w∈Σ∗, then we call f as computable function.

What is a non-computable function?

Yet there are also problems and functions that that are non-computable (or undecidable or uncomputable), meaning that there exists no algorithm that can compute an answer or output for all inputs in a finite number of simple steps.

What does it means for an algorithm to be effectively computable?

is effectively computable if there is an effective procedure or algorithm that correctly calculates f. An effective procedure is one that meets the following specifications.

What are computable predicates?

A function whose value can be calculated by some Turing machine in a finite number of steps. Also known as effectively computable function.

What is Turing computable function TOC?

A function is Turing computable if the function’s value can be computed with a Turing machine . More specifically, let D be a set of words in a given alphabet and let f be a function which maps elements of D to words on the same alphabet.

Which problems are not computable?

A non-computable is a problem for which there is no algorithm that can be used to solve it. An example of a non-computable is the halting problem. Hyper computation is more powerful than a Turing Machine and has the capability of solving problems that the Turing Machine can’t.

What is computable problem?

Computability is the ability to solve a problem in an effective manner. It is a key topic of the field of computability theory within mathematical logic and the theory of computation within computer science. The computability of a problem is closely linked to the existence of an algorithm to solve the problem.

What is Turing computable function define recursive function?

According to the Church–Turing thesis, computable functions are exactly the functions that can be calculated using a mechanical calculation device given unlimited amounts of time and storage space. The Blum axioms can be used to define an abstract computational complexity theory on the set of computable functions.