R. Raz, G. Tardos, O. Verbitsky, and N. Vereshchagin. Arthur-Merlin games in Boolean decision trees, J. Cornput. Sys. Sci. 59(2):346-372, 1999. Home/Search Document Details and Download
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Quantum Certificate Complexity - Aaronson (Correct)
....the minimum expected number of queries used by a randomized verifier for X, and RC (f) is the maximum ofRC x (f) over all X. We define QC (f) analogously, with quantum instead of randomized algorithms. The following justifies the defin ition (the RC (f) part was originally shown by Raz et al. [15]) IThroughout this paper, we use Y to denote the actual input being queried, and X to denote the claimed input (whose randomized certificate complexity, block sensitivity, and so on we want to study) Proposition4 Making the error probability two sided rather than one sided changes RC (f) ....
....6, we exhibit asymptotic gaps be tween RC (f) and other query complexity measures, in cluding a total f for which C(f) O (QC(f)2 25) and a symmetric partial f for which QC (f) O (1) yet Q2 (f) f] n log n) We conclude in Section 7 with some open problems. 3. Related Work Raz et al. [15] studied a query complexity measure they called ma (f) for Merlin Arthur. In our notation, ma (f) equals the maximum of RC x (f) over all X with f (X) 1. Raz et al. observed that ma (f) ip (f) where ip (f) is the number of queries needed given arbitrarily many rounds of interaction with a ....
R. Raz, G. Tardos, O. Verbitsky, and N. Vereshchagin. Arthur-Merlin games in Boolean decision trees, J. Cornput. Sys. Sci. 59(2):346-372, 1999.
Quantum Certificate Complexity - Aaronson (Correct)
....minimum expected number of queries used by a randomized ver ifier for X, and Re (f) is the maximum of Re X (f) over all X. We define QC (f) analogously, with quantum in stead of raudomized algorithms. The following jus tifies the definition (the RC (f) part was originally shown by Raz et at. [15]) Proposition 4 Making the error probability two sided rather than one sided changes RC(f) and QC (f) by at most a constant factor. Proof. For RC (f) let r[ be the event that verifier V rejects on input Y, and let d[ be the event that V encounters a disagreement with X on Y. We may assume Pr ....
....Section 6, we exhibit asymptotic gaps between RC (f) and other quew complexity menures, includ ing a total f for which C (f) O (QC (f)2.20) and a symmetric partial f for which QC (f) O (1) yet Q2 (f) f (n log n) We conclude in Section 7 with some open problems. 3 Related Work Raz et al. [15] studied a query complexity measure they called ma (f) for Merlin Arthur. In our no tation, ma (f) equals the maximum of RC X (f) over all X with f(X) 1. Raz et al. observed that ma (f) ip (f) where ip (f) is the number of queries needed given arbitrarily many rounds of interaction with a ....
R. Raz, G. Tardos, O. Verbitsky, and N. Vereshchagin. Arthur-Merlin games in Boolean decision trees, J. Cornput. Sys. Sci. 59(2):346- 372, 1999.
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