hwsol5.3 - R L n-1 When the computation of R L n-1 is...

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CSci 5403, Spring 2010 Stefan Nelson-Lindall Example Solution 5.3 Candidate 3. Onward and Downward. For any language L , define the language L n = { x : x L ∧ | x | ≤ n } . Say that L is downward self-reducible if there exists a polynomial-time OTM R such that R L n - 1 decides L n . Prove that if L is downward self-reducible then L PSPACE . Pf: By construction, if L n is downward self-reducible, there exists a PSPACE machine M that decides L n . Let M simulate the computation of R L n , with the exception that when the oracle is queried, it saves its state and begins simulating
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Unformatted text preview: R L n-1 . When the computation of R L n-1 is complete, this value is returned as the result of the “oracle” call. There are no strings of negative length, so calls to the oracle L-1 may safely be rejected. R L n ∈ P ⊂ PSPACE , so the total memory usage is ≤ ( n + 1) * n c = O ( n c +1 ) ⊂ PSPACE . M decides L n and M ∈ PSPACE , therefore L n ∈ PSPACE . ± 1...
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