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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 34 (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,
Locally Random Reductions in Interactive Complexity Theory
 DIMACS Series in Discrete Mathematics and Theoretical Computer Science
, 1993
"... We survey definitions, known results, and open questions in the area of locally random reductions and explore the ramifications of these reductions in complexity theory. This paper is based on a survey talk given at the DIMACS Workshop on Structural Complexity and Cryptography, Rutgers University, ..."
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Cited by 24 (5 self)
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We survey definitions, known results, and open questions in the area of locally random reductions and explore the ramifications of these reductions in complexity theory. This paper is based on a survey talk given at the DIMACS Workshop on Structural Complexity and Cryptography, Rutgers University, New Brunswick NJ, December 1990. 1 Introduction We consider the question of whether a probabilistic polynomialtime machine A can compute a function f in the following manner. A interacts with one or more machines B 1 , . . ., B k that are not restricted to probabilistic polynomial time. At the end of the interaction, A can use the information obtained from the B i 's to compute f(x). However, the information that A sends to the B i 's is locally random. Informally, this means that no individual B i can use it to figure out what A's private input x is. This study can be motivated by the practical problem of using shared resources for private computations. For example, f may be a financial ...
Languages that are Easier than their Proofs
, 1991
"... 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 reduc ..."
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Cited by 13 (7 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. Similarly we present languages where checking is harder than computing membership. Each of the following properties  checkability, randomselfreducibility, reduction from search to decision, and interactive proofs in which the prover's power is limited to deciding membership in the language itself  implies coherence, one of the weakest forms of selfreducibility. Under assumptions about tripleexponential time, we construct incoherent sets in NP....
Hiding Instances in ZeroKnowledge Proof Systems (Extended Abstract)
 ADVANCES IN CRYPTOLOGY  CRYPTO '90, LECTURE NOTES IN COMPUTER SCIENCE
, 1990
"... Informally speaking, an instancehiding proof system for the function f is a protocol in which a polynomialtime verifier is convinced of the value of f(x) but does not reveal the input x to the provers. We show here that a boolean function f has an instancehiding proof system if and only if it ..."
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Cited by 6 (0 self)
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Informally speaking, an instancehiding proof system for the function f is a protocol in which a polynomialtime verifier is convinced of the value of f(x) but does not reveal the input x to the provers. We show here that a boolean function f has an instancehiding proof system if and only if it is the characteristic function of a language in NEXP " coNEXP. We formalize the notion of zeroknowledge for instancehiding proof systems with several provers and show that all such systems can be made perfect zeroknowledge.
InstanceHiding Proof Systems
, 1993
"... We define the notion of an instancehiding proof system (ihps) for a function f ; informally, an ihps is a protocol in which a polynomialtime verifier interacts with one or more allpowerful provers and is convinced of the value of f(x) but does not reveal the input x to the provers. We show here t ..."
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Cited by 2 (0 self)
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We define the notion of an instancehiding proof system (ihps) for a function f ; informally, an ihps is a protocol in which a polynomialtime verifier interacts with one or more allpowerful provers and is convinced of the value of f(x) but does not reveal the input x to the provers. We show here that a function f has a multiprover ihps if and only if it is computable in FNEXP. We formalize the notion of zeroknowledge for ihps's and show that any function that has a multiprover ihps in fact has one that is perfect zeroknowledge. Under the assumption that oneway permutations exist, we show that f has a oneprover, zeroknowledge ihps if and only if it is in FPSPACE and has a oneoracle instancehiding scheme (ihs).
The Use of Coding Theory in Computational Complexity
 In Proceedings of Symposia in Applied Mathematics, R. Calderbank (ed.), American Mathematics Society, Providence
, 1995
"... The interplay of coding theory and computational complexity theory is a rich source of results and problems. This article surveys three of the major themes in this area: ffl the use of codes to improve algorithmic efficiency ffl the theory of program testing and correcting, which is a complexity ..."
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The interplay of coding theory and computational complexity theory is a rich source of results and problems. This article surveys three of the major themes in this area: ffl the use of codes to improve algorithmic efficiency ffl the theory of program testing and correcting, which is a complexity theoretic analogue of error detection and correction ffl the use of codes to obtain characterizations of traditional complexity classes such as NP and PSPACE; these new characterizations are in turn used to show that certain combinatorial optimization problems are as hard to approximate closely as they are to solve exactly. 1 Introduction Complexity theory is the study of efficient computation. Faced with a computational problem that can be modelled formally, a complexity theorist seeks first to find a solution that is provably efficient and, if such a solution is not found, to prove that none exists. Coding theory, which provides techniques for "robust representation" of information, ...