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2. We proved that TQBF is PSPACE-complete. We can use this to give a second proof that PSPACE = NPSPACE, by proving that TQBF is also a NPSPACE complete problem. For this problem, do not assume PSPACE = NPSPACE by Savitch's theorem, as that is what we are trying to prove, you may only assume PSPACE C NPSPACE. (a) (5 points) Prove that TQBF = NPSPACE (Hint, you should not be able to show that TQBF € NP). (b) (5 points) We proved that VL € PSPACE that L<, TQBF. Explain how you could modify the proof we did to show that VL € NPSPACE that LS, TQBF (Hint, why could we show SAT complete for a nondeterministic class, and TQBF complete for a deterministic one?)

2. We proved that TQBF is PSPACE-complete. We can use this to give a second proof that PSPACE = NPSPACE, by proving that TQBF is also a NPSPACE complete problem. For this problem, do not assume PSPACE = NPSPACE by Savitch's theorem, as that is what we are trying to prove, you may only assume PSPACE C NPSPACE. (a) (5 points) Prove that TQBF = NPSPACE (Hint, you should not be able to show that TQBF € NP). (b) (5 points) We proved that VL € PSPACE that L<, TQBF. Explain how you could modify the proof we did to show that VL € NPSPACE that LS, TQBF (Hint, why could we show SAT complete for a nondeterministic class, and TQBF complete for a deterministic one?)

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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2. We proved that TQBF is PSPACE-complete. We can use this to give a second proof that PSPACE = NPSPACE, by proving that TQBF is also a NPSPACE complete problem. For this problem, do not assume PSPACE = NPSPACE by Savitch's theorem, as that is what we are trying to prove, you may only assume PSPACE C NPSPACE. (a) (5 points) Prove that TQBF = NPSPACE (Hint, you should not be able to show that TQBF € NP). (b) (5 points) We proved that VL € PSPACE that L<, TQBF. Explain how you could modify the proof we did to show that VL € NPSPACE that LS, TQBF (Hint, why could we show SAT complete for a nondeterministic class, and TQBF complete for a deterministic one?)
Transcribed Image Text:2. We proved that TQBF is PSPACE-complete. We can use this to give a second proof that PSPACE = NPSPACE, by proving that TQBF is also a NPSPACE complete problem. For this problem, do not assume PSPACE = NPSPACE by Savitch's theorem, as that is what we are trying to prove, you may only assume PSPACE C NPSPACE. (a) (5 points) Prove that TQBF = NPSPACE (Hint, you should not be able to show that TQBF € NP). (b) (5 points) We proved that VL € PSPACE that L<, TQBF. Explain how you could modify the proof we did to show that VL € NPSPACE that LS, TQBF (Hint, why could we show SAT complete for a nondeterministic class, and TQBF complete for a deterministic one?)
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