Speedup theorem (original) (raw)

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Computational theorem

For the theorem that some mathematical proofs can be drastically shortened in stronger axiom systems, see Gödel's speed-up theorem.

In computational complexity theory, a speedup theorem is a theorem that for any algorithm (of a certain class) demonstrates the existence of a more efficient algorithm solving the same problem.

Examples:

• Linear speedup theorem, that the space and time requirements of a Turing machine solving a decision problem can be reduced by a multiplicative constant factor.
• Blum's speedup theorem, which provides speedup by any computable function (not just linear, as in the previous theorem).
• Amdahl's law, the theoretical speedup in latency of the execution of a task at a fixed workload that can be expected of a system whose resources are improved.