The Sipser-Lautemann Theorem, established in 1983 through the work of Michael Sipser, Peter Gacs and Clemens Lautemann, shows that the complexity class BPP, of problems solvable by randomized algorithms with bounded error, is contained within the second level of the polynomial hierarchy, specifically inside the intersection of Sigma-2 and Pi-2. The result places probabilistic polynomial-time computation inside a well understood deterministic hierarchy, though it falls short of the stronger conjecture that BPP equals P, which would mean randomization gives no extra computational power at all.
Facts
StatementBounded-error probabilistic polynomial time (BPP) is contained in the polynomial time hierarchy, and more specifically in Sigma-2 intersect Pi-2. 1 Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
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In Branch
Source Sipser-Lautemann theorem, Wikipedia
Sources
1. Sipser-Lautemann theorem, Wikipedia
Lead paragraph
Bounded-error probabilistic polynomial (BPP) time is contained in the polynomial time hierarchy, and more specifically Σ2 ∩ Π2.
History paragraph
In 1983, Michael Sipser showed that BPP is contained in the polynomial time hierarchy.
- In Branch: Computational Complexity Theory, Lead sentence
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