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The knowledge complexity of interactive proof systems

, 1989
"... Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/nonHamiltonian. In th ..."
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Cited by 1246 (39 self)
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Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian
Guide to Elliptic Curve Cryptography
, 2004
"... Elliptic curves have been intensively studied in number theory and algebraic geometry for over 100 years and there is an enormous amount of literature on the subject. To quote the mathematician Serge Lang: It is possible to write endlessly on elliptic curves. (This is not a threat.) Elliptic curves ..."
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Cited by 610 (18 self)
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Elliptic curves have been intensively studied in number theory and algebraic geometry for over 100 years and there is an enormous amount of literature on the subject. To quote the mathematician Serge Lang: It is possible to write endlessly on elliptic curves. (This is not a threat.) Elliptic curves
Proofs that Yield Nothing but Their Validity or All Languages in NP Have ZeroKnowledge Proof Systems
 JOURNAL OF THE ACM
, 1991
"... In this paper the generality and wide applicability of Zeroknowledge proofs, a notion introduced by Goldwasser, Micali, and Rackoff is demonstrated. These are probabilistic and interactive proofs that, for the members of a language, efficiently demonstrate membership in the language without convey ..."
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Cited by 427 (43 self)
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In this paper the generality and wide applicability of Zeroknowledge proofs, a notion introduced by Goldwasser, Micali, and Rackoff is demonstrated. These are probabilistic and interactive proofs that, for the members of a language, efficiently demonstrate membership in the language without
The Foundation of a Generic Theorem Prover
 Journal of Automated Reasoning
, 1989
"... Isabelle [28, 30] is an interactive theorem prover that supports a variety of logics. It represents rules as propositions (not as functions) and builds proofs by combining rules. These operations constitute a metalogic (or `logical framework') in which the objectlogics are formalized. Isabell ..."
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Cited by 471 (48 self)
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Isabelle [28, 30] is an interactive theorem prover that supports a variety of logics. It represents rules as propositions (not as functions) and builds proofs by combining rules. These operations constitute a metalogic (or `logical framework') in which the objectlogics are formalized
Algebraic Methods for Interactive Proof Systems
, 1990
"... We present a new algebraic technique for the construction of interactive proof systems. We use our technique to prove that every language in the polynomialtime hierarchy has an interactive proof system. This technique played a pivotal role in the recent proofs that IP=PSPACE (Shamir) and that MIP ..."
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Cited by 338 (28 self)
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We present a new algebraic technique for the construction of interactive proof systems. We use our technique to prove that every language in the polynomialtime hierarchy has an interactive proof system. This technique played a pivotal role in the recent proofs that IP=PSPACE (Shamir
ReTiling Polygonal Surfaces
 Computer Graphics
, 1992
"... This paper presents an automatic method of creating surface models at several levels of detail from an original polygonal description of a given object. Representing models at various levels of detail is important for achieving high frame rates in interactive graphics applications and also for speed ..."
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Cited by 445 (3 self)
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This paper presents an automatic method of creating surface models at several levels of detail from an original polygonal description of a given object. Representing models at various levels of detail is important for achieving high frame rates in interactive graphics applications and also
NonDeterministic Exponential Time has TwoProver Interactive Protocols
"... We determine the exact power of twoprover interactive proof systems introduced by BenOr, Goldwasser, Kilian, and Wigderson (1988). In this system, two allpowerful noncommunicating provers convince a randomizing polynomial time verifier in polynomial time that the input z belongs to the language ..."
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Cited by 416 (37 self)
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We determine the exact power of twoprover interactive proof systems introduced by BenOr, Goldwasser, Kilian, and Wigderson (1988). In this system, two allpowerful noncommunicating provers convince a randomizing polynomial time verifier in polynomial time that the input z belongs
Active Perception
, 1988
"... Active Perception (Active Vision specifically) is defined as a study of Modeling and Control strategies for perception. By modeling we mean models of sensors, processing modules and their interaction. We distinguish local models from global models by their extent of application in space and time. T ..."
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Cited by 431 (12 self)
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Active Perception (Active Vision specifically) is defined as a study of Modeling and Control strategies for perception. By modeling we mean models of sensors, processing modules and their interaction. We distinguish local models from global models by their extent of application in space and time
Policy gradient methods for reinforcement learning with function approximation.
 In NIPS,
, 1999
"... Abstract Function approximation is essential to reinforcement learning, but the standard approach of approximating a value function and determining a policy from it has so far proven theoretically intractable. In this paper we explore an alternative approach in which the policy is explicitly repres ..."
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Cited by 439 (20 self)
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;actorcritic" or policyiteration architectures (e.g., Policy Gradient Theorem We consider the standard reinforcement learning framework (see, e.g., Sutton and Barto, 1998), in which a learning agent interacts with a Markov decision process (MDP). The state, action, and reward at each time t ∈ {0, 1, 2
Mobile Values, New Names, and Secure Communication
, 2001
"... We study the interaction of the "new" construct with a rich but common form of (firstorder) communication. This interaction is crucial in security protocols, which are the main motivating examples for our work; it also appears in other programminglanguage contexts. Specifically, we intro ..."
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Cited by 372 (17 self)
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We study the interaction of the "new" construct with a rich but common form of (firstorder) communication. This interaction is crucial in security protocols, which are the main motivating examples for our work; it also appears in other programminglanguage contexts. Specifically, we
Results 1  10
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