Which of the following best explains the ability to solve problems algorithmically?

Which of the following best explains the ability to solve problems algorithmically?

(A) Any problem can be solved algorithmically, though some algorithmic solutions may require humans to validate the results.

(B) Any problem can be solved algorithmically, though some algorithmic solutions must be executed on multiple devices in parallel.

(C) Any problem can be solved algorithmically, though some algorithmic solutions require a very large amount of data storage to execute

(D) There exist some problems that cannot be solved algorithmically using any computer.

Answer: (D) There exist some problems that cannot be solved algorithmically using any computer.

This statement describes the notion of undecidability in computer science and the theory of computation usually taught to every computer science student. It is in routine practice that there are things that just cannot be done or resolved by an algorithm, no matter how powerful the computer is and how many resources are at the programmer’s or analyst’s disposal.

An undecidable problem that many people are familiar with is the “halting problem.” Turing suggested the issue in 1936 and informed whether a program intended as input would cease to execute or would indefinitely continue. Turing then showed that no computable function can solve this problem for all programs and all the inputs that can be provided. Another example is the so-called “busy beaver problem”, which requires finding the value of the greatest number of steps that a Turing machine, containing exactly s states, can make before halting. However, as the number of states grows, this problem turns into a type of undecidable problem. The above examples show that, no matter how sophisticated technology becomes, there are absolute barriers to the algorithmizing of certain problems. However, it is also necessary to notice that the existence of undecidable practical problems proves the existence of practical problems’ solutions effectively and also shows the limitations of the algorithmic approach and the potential capabilities of the computational technology. Indeed, this understanding is important for computer scientists and programmers as it defines algorithms and the approach to problem-solving in the different fields of computer science and applications.