3.18 Undecidable Problems
1. Exam Points
- For undecidable problems: There exist problems that no algorithm will ever be able to solve for all possible inputs.
计算机不是万能的，总有它无法解决的问题。
2. Knowledge Points
(1) Undecidable Problems
There exist problems that computers cannot solve, and even when a computer can solve a problem, it may not be able to do so in a reasonable amount of time.- A
decidable problem is a decision problem for which an algorithm can be written to produce a correct output for all inputs (e.g., “Is the number even?”).
- An
undecidable problem is one for which no algorithm can be constructed that is always capable of providing a correct yes-or-no answer.
- An
undecidable problem may have some instances that have an algorithmic solution, but there is no algorithmic solution that could solve all instances of the problem.
3. Exercises
