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Halting Problem

Definition

The halting problem refers to the question of whether an arbitrary program will halt (terminate) or run forever when executed on some input.

Analogy

Imagine you have a robot vacuum cleaner that sometimes gets stuck in loops and keeps moving back and forth without ever stopping. You want to know if it will eventually stop cleaning or keep going forever. This is similar to the halting problem, where we try to determine if a program will eventually finish its execution or continue indefinitely.

Related terms

Decidable Problem: A decidable problem is a computational problem for which there exists an algorithm that can determine whether a given input has a specific property or satisfies a certain condition.

Undecidable Problem: An undecidable problem is a computational problem for which no algorithm can determine whether a given input has a specific property or satisfies a certain condition.

Turing Machine: A Turing machine is an abstract mathematical model used to simulate any computer algorithm. It consists of an infinite tape divided into cells, and the machine can read, write, and move along the tape based on its current state.