Space Hierarchy Results for Randomized and other Semantic Models
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There exists a language computable by two-sided error randomized machines using s′(n) space and one bit of advice that is not computable by two-sided error randomized machines using s(n) space and min(s(n), n) bits of advice.
There exists a language computable by zero-sided error randomized machines in space s′(n) with one bit of advice that is not computable by one-sided error randomized machines using s(n) space and min(s(n), n) bits of advice.
If, in addition, s(n) = O(n) then the condition on s′ above can be relaxed to s′(n) = ω(s(n + 1)). This yields tight space hierarchies for typical space bounds s(n) that are at most linear.
We also obtain results that apply to generic semantic models of computation.
Keywords.Space hierarchy randomized computations computations with advice promise classes semantic models
Subject classification.68Q15 68Q10 03D15 68Q25
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