1. Let's start by understanding what a decidable problem is. 2. A decidable problem is a decision problem for which there exists an algorithm that can determine the answer (yes or no) for any given input in a finite amount of time. 3. In other words, for decidable problems, we can always compute the exact solution using an algorithm. 4. Example of a decidable problem: "Given a number, is it even?" There is a straightforward algorithm to check if a number is even. 5. Now, let's discuss undecidable problems. 6. An undecidable problem is a decision problem for which no algorithm can decide the answer for all possible inputs within finite time. 7. This means there is no general algorithmic solution that can always give the correct yes/no answer. 8. Famous example of an undecidable problem: The Halting Problem. It asks: "Given a program and input, will the program eventually stop running or run forever?" This problem cannot be solved by any algorithm. 9. To summarize: - Decidable problems have algorithmic solutions that always terminate. - Undecidable problems have no such algorithm that works for every input.