Oblivious Symmetric Alternation

Chakaravarthy, Venkatesan T.; Roy, Sambuddha

doi:10.1007/11672142_18

Cited by 12 publications

(10 citation statements)

References 16 publications

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“…Chakaravarthy and Roy [5] considered an input-oblivious version of the symmetric alternation class S 2 , and showed that this new class, denoted O 2 , contains BPP. They also showed that if N P ⊂ P/poly, then the Polynomial-time Hierarchy collapses to O 2 .…”

Section: Other Input-oblivious Proof Systemsmentioning

confidence: 99%

“…5 This definition requires efficient simulation of the (prescribed) verifier's view of the interaction, based solely on the verifier's actual input. (Indeed, here we refer to the verifier as the combination of the two stages, denoted V 1 and V 2 , and note that this combined verifier gets the actual input (rather than merely its length).)…”

Section: Input-oblivious Zkmentioning

confidence: 99%

“…4 Such constructions are presented in [9,12,13,17]. 5 The standard (complexity theoretic) definition of zero-knowledge requires efficient simulation of the view of the prescribed verifier (of the interaction with the prover); a stronger definition, commonly used in cryptography (cf. [7,Sec.…”

Section: Input-oblivious Zkmentioning

confidence: 99%

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Input-Oblivious Proof Systems and a Uniform Complexity Perspective on P/poly

Goldreich

Meir

2015

ACM Trans. Comput. Theory

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An input-oblivious proof system is a proof system in which the proof does not depend on the claim being proved. Input-oblivious versions of N P and MA were introduced in passing by Fortnow, Santhanam, and Williams (CCC 2009), who also showed that those classes are related to questions on circuit complexity.In this note we wish to highlight the notion of input-oblivious proof systems, and initiate a more systematic study of them. We begin by describing in detail the results of Fortnow et al., and discussing their connection to circuit complexity. We then extend the study to inputoblivious versions of IP, PCP, and ZK, and present few preliminary results regarding those versions.

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Section: Other Input-oblivious Proof Systemsmentioning

confidence: 99%

Section: Input-oblivious Zkmentioning

confidence: 99%

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Input-Oblivious Proof Systems and a Uniform Complexity Perspective on P/poly

Goldreich

Meir

2015

ACM Trans. Comput. Theory

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“…This notion has been studied before: Chakaravarthy and Roy [16] and Fortnow and Santhanam [17] defined the complexity class ONP ('Oblivious NP'), which is like NP except that the witness can depend only on the input length. Independently, Aaronson [5] defined the complexity class YP, 6 which is easily seen to equal ONP ∩ coONP.…”

Section: Theorem 15 ([10])mentioning

confidence: 99%

A full characterization of quantum advice

Aaronson

Drucker

2010

Proceedings of the Forty-Second ACM Symposium on Theory of Computing

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We prove the following surprising result: given any quantum state ρ on n qubits, there exists a local Hamiltonian H on poly (n) qubits (e.g., a sum of two-qubit interactions), such that any ground state of H can be used to simulate ρ on all quantum circuits of fixed polynomial size. In terms of complexity classes, this implies that BQP/qpoly ⊆ QMA/poly, which supersedes the previous result of Aaronson that BQP/qpoly ⊆ PP/poly. Indeed, we can exactly characterize quantum advice, as equivalent in power to untrusted quantum advice combined with trusted classical advice.Proving our main result requires combining a large number of previous tools-including a result of Alon et al. on learning of real-valued concept classes, a result of Aaronson on the learnability of quantum states, and a result of Aharonov and Regev on 'QMA + super-verifiers'-and also creating some new ones. The main new tool is a so-called majority-certificates lemma, which is closely related to boosting in machine learning, and which seems likely to find independent applications. In its simplest version, this lemma says the following. Given any set S of Boolean functions on n variables, any function f ∈ S can be expressed as the pointwise majority of m = O (n) functions f 1 , . . . , f m ∈ S, such that each f i is the unique function in S compatible with O (log |S|) input/output constraints.

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“…We explore the class ONP, "Oblivious NP", implicitly defined by Chakaravarthy and Roy [CR06]. A language L is in ONP if for every n there is a single polynomialsize witness w n , for every x in L with |x| = n. Thus ONP is a rather restrictive subclass of NP.…”

Section: Introductionmentioning

confidence: 99%

Fixed-Polynomial Size Circuit Bounds

Fortnow

Santhanam

Williams

2009

2009 24th Annual IEEE Conference on Computational Complexity

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Abstract-InWe explore questions about fixed-polynomial size circuit lower bounds around and beyond the algebrization barrier. We find several connections, including• The following are equivalent:where ONP is the class of languages accepted obliviously by NP machines, with witnesses for "yes" instances depending only on the input length.• For a large number of natural classes C and all k 1, C is in SIZE(n k ) if and only if C/1 ∩ P/poly is in SIZE(n k ).• If there is a d such that MATIME(n) ⊆ NTIME(n d ), then P NP does not have O(n k ) size circuits for any k > 0.• One cannot show n 2 -size circuit lower bounds for ⊕P without new nonrelativizing techniques. In particular, the proof that PP ⊆ SIZE(n k ) for all k relies on the (relativizing) result that P PP ⊆ MA =⇒ PP ⊆ SIZE(n k ), and we give an oracle relative to which P ⊕P ⊆ MA and ⊕P ⊆ SIZE(n 2 ) both hold.

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Oblivious Symmetric Alternation

Cited by 12 publications

References 16 publications

Input-Oblivious Proof Systems and a Uniform Complexity Perspective on P/poly

Input-Oblivious Proof Systems and a Uniform Complexity Perspective on P/poly

A full characterization of quantum advice

Fixed-Polynomial Size Circuit Bounds

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