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Undecidable Problem

Definition

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.

Analogy

Imagine trying to find out if there's life on other planets by using only your eyes. No matter how hard you look, you won't be able to definitively prove or disprove it. Similarly, undecidable problems cannot be solved with any algorithm because they lack definitive answers.

Related terms

Decidable Problem: A decidable problem is the opposite of an undecidable problem; it refers to computational problems for which there exists an algorithm that can determine whether a given input has a specific property or satisfies a certain condition.

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

Gödel's Incompleteness Theorems: These theorems, proved by Kurt Gödel, state that in any formal system of mathematics, there will always be true statements that cannot be proven within the system itself.