A zero-one SUBEXP-dimension law for BPP
Philippe Moser
TL;DR
This paper establishes a dichotomy in computational complexity, showing that BPP either has very low SUBEXP-dimension, indicating easy randomness, or it equals EXP, implying intractable randomness.
Contribution
It proves a zero-one SUBEXP-dimension law for BPP, revealing a fundamental complexity classification.
Findings
BPP has either SUBEXP-dimension zero or BPP=EXP
Randomness in BPP is either easy or intractable
The result establishes a sharp complexity dichotomy
Abstract
We show that BPP has either SUBEXP-dimension zero (randomness is easy) or BPP=EXP (randomness is intractable).
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Artificial Intelligence in Games · Advanced Topology and Set Theory