Blum's Speedup Theorem, stated by Manuel Blum in 1967, shows that for any abstract measure of computational complexity there exists a computable function with no single optimal program: for every program computing the function, another program exists computing it with markedly lower complexity, and this speedup can be made arbitrarily large, for example quadratically or exponentially smaller. The theorem means that, unlike for many specific problems, no definitive complexity can be assigned to an arbitrary computable function, since a still-faster program can always in principle be found.
Facts
StatementFor any complexity measure there is a computable function with no optimal program, because every program has a program of lower complexity. 1 Classification
Statement Form Connections
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Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Source Blum's speedup theorem, Wikipedia
Sources
1. Blum's speedup theorem, Wikipedia
Lead paragraph, first sentence
Blum's speedup theorem, first stated by Manuel Blum in 1967, is a fundamental theorem about the complexity of computable functions.
Lead paragraph, implication
for any complexity measure, there exists a computable function such that there is no optimal program computing it, because every program has a program of lower complexity.
In Branch: Computational Complexity Theory, Lead sentence
In computational complexity theory, Blum's speedup theorem, first stated by Manuel Blum in 1967, is a fundamental theorem about th
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