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The complexity of decision versus search
 SIAM Journal on Computing
, 1994
"... A basic question about NP is whether or not search reduces in polynomial time to decision. We indicate that the answer is negative: under a complexity assumption (that deterministic and nondeterministic doubleexponential time are unequal) we construct a language in NP for which search does not red ..."
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Cited by 32 (1 self)
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A basic question about NP is whether or not search reduces in polynomial time to decision. We indicate that the answer is negative: under a complexity assumption (that deterministic and nondeterministic doubleexponential time are unequal) we construct a language in NP for which search does not reduce to decision. These ideas extend in a natural way to interactive proofs and program checking. Under similar assumptions we present languages in NP for which it is harder to prove membership interactively than it is to decide this membership, and languages in NP which are not checkable. Keywords: NPcompleteness, selfreducibility, interactive proofs, program checking, sparse sets,
Uniform Generation of NPwitnesses using an NPoracle
 Information and Computation
, 1997
"... A Uniform Generation procedure for NP is an algorithm which given any input in a fixed NPlanguage, outputs a uniformly distributed NPwitness for membership of the input in the language. We present a Uniform Generation procedure for NP that runs in probabilistic polynomialtime with an NPoracle. T ..."
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Cited by 24 (1 self)
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A Uniform Generation procedure for NP is an algorithm which given any input in a fixed NPlanguage, outputs a uniformly distributed NPwitness for membership of the input in the language. We present a Uniform Generation procedure for NP that runs in probabilistic polynomialtime with an NPoracle. This improves upon results of Jerrum, Valiant and Vazirani, which either require a \Sigma P 2 oracle or obtain only almost uniform generation. Our procedure utilizes ideas originating in the works of Sipser, Stockmeyer, and Jerrum, Valiant and Vazirani. Dept. of Computer Science & Engineering, University of California at San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA. EMail: mihir@cs.ucsd.edu. URL: http://wwwcse.ucsd.edu/users/mihir. Supported in part by NSF CAREER Award CCR9624439 and a 1996 Packard Foundation Fellowship in Science and Engineering. y Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel. EMail: oded@wis...
On the complexity of interactive proofs with bounded communication
 Information Processing Letters
, 1998
"... We investigate the computational complexity of languages which haveinteractive proof systems of bounded message complexity. In particular, denoting the length of the input by n, we show that If L has an interactive proof in which the total communication is bounded by c(n) bits then L can be recogniz ..."
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Cited by 19 (1 self)
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We investigate the computational complexity of languages which haveinteractive proof systems of bounded message complexity. In particular, denoting the length of the input by n, we show that If L has an interactive proof in which the total communication is bounded by c(n) bits then L can be recognized by a probabilistic machine in time exponential in O(c(n)+log(n)). If L has a publiccoin interactive proof in which the prover sends c(n) bits then L can be recognized by a probabilistic machine in time exponential in O(c(n) log(c(n)) + log(n)). If L has an interactive proof in which the prover sends c(n) bits then L can be recognized by a probabilistic machine with an NPoracle in time exponential in O(c(n) log(c(n)) + log(n)). Work done while being on a sabbatical leave at LCS, MIT. 0 1
On the Role of Shared Randomness in Two Prover Proof Systems
, 1995
"... In this paper we consider which aspects of the two prover model are necessary for their striking language recognition and zeroknowledge capabilities. We approach this question by looking at an alternative, more symmetric model which we call the double verifier model. We find that in this model the ..."
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Cited by 3 (2 self)
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In this paper we consider which aspects of the two prover model are necessary for their striking language recognition and zeroknowledge capabilities. We approach this question by looking at an alternative, more symmetric model which we call the double verifier model. We find that in this model the shared randomness of the verifiers is key to the language recognition power: if the verifiers don't share randomness the power is PSPACE; otherwise it is MIP = NEXPTIME. We find that the shared randomness of the provers is necessary for zeroknowledge: if the provers don't share randomness, statistical zeroknowledge is only possible for languages in BPP NP ; else it is possible for all of NEXPTIME. These results have immediate implications for the standard twoprover model. We see that correlations between the verifier's queries is crucial for the language recognition power of two prover proofs. In particular, the natural analog of IP = AM does not hold in the twoprover model unless NEX...