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The knowledge complexity of interactive proof systems

by Shafi Goldwasser, Silvio Micali, Charles Rackoff - , 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/non-Hamiltonian. In th ..."
Abstract - Cited by 1246 (39 self) - Add to MetaCart
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

Algebraic Methods for Interactive Proof Systems

by Carsten Lund, Lance Fortnow, Howard Karloff, Noam Nisan , 1990
"... We present a new algebraic technique for the construc-tion of interactive proof systems. We use our technique to prove that every language in the polynomial-time hierarchy has an interactive proof system. This tech-nique played a pivotal role in the recent proofs that IP=PSPACE (Shamir) and that MIP ..."
Abstract - Cited by 338 (28 self) - Add to MetaCart
We present a new algebraic technique for the construc-tion of interactive proof systems. We use our technique to prove that every language in the polynomial-time hierarchy has an interactive proof system. This tech-nique played a pivotal role in the recent proofs that IP=PSPACE (Shamir

INTERACTIVE PROOFS

by Akhil Mathew
"... Abstract. These are notes from a Mathtable talk I gave. You and I share two large graphs. Waving my magic wand, I discover that they are not isomorphic and rush to tell you. You don’t believe me and demand proof; however, as a busy undergraduate, you insist that the proof be verifiable in polynomial ..."
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in that if I lie, you’ll probably detect it. Moreover, with such ”interactive proofs ” I can efficiently convince you of the right answer for a large class of computationally difficult problems. I will attempt to convince you of this 1992 result; random bits not required. 1.

Interactive proofs and the hardness of approximating cliques

by Uriel Feige, Shafi Goldwasser, Laszlo Lovasz, Shmuel Safra, Mario Szegedy - JOURNAL OF THE ACM , 1996
"... The contribution of this paper is two-fold. First, a connection is shown between approximating the size of the largest clique in a graph and multi-prover interactive proofs. Second, an efficient multi-prover interactive proof for NP languages is constructed, where the verifier uses very few random b ..."
Abstract - Cited by 170 (11 self) - Add to MetaCart
The contribution of this paper is two-fold. First, a connection is shown between approximating the size of the largest clique in a graph and multi-prover interactive proofs. Second, an efficient multi-prover interactive proof for NP languages is constructed, where the verifier uses very few random

Interactive Coding for Interactive Proofs

by Yevgeniy Dodis, Allison Bishop Lewko
"... We consider interactive proof systems over adversarial communication channels. We show that the seminal result that IP = PSPACE still holds when the communication channel is malicious, allowing even a constant fraction of the communication to be arbitrarily corrupted. 1 ..."
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We consider interactive proof systems over adversarial communication channels. We show that the seminal result that IP = PSPACE still holds when the communication channel is malicious, allowing even a constant fraction of the communication to be arbitrarily corrupted. 1

Delegating computation: interactive proofs for muggles

by Shafi Goldwasser, Yael Tauman Kalai, Guy N. Rothblum - In Proceedings of the ACM Symposium on the Theory of Computing (STOC , 2008
"... In this work we study interactive proofs for tractable languages. The (honest) prover should be efficient and run in polynomial time, or in other words a “muggle”. 1 The verifier should be super-efficient and run in nearly-linear time. These proof systems can be used for delegating computation: a se ..."
Abstract - Cited by 113 (6 self) - Add to MetaCart
In this work we study interactive proofs for tractable languages. The (honest) prover should be efficient and run in polynomial time, or in other words a “muggle”. 1 The verifier should be super-efficient and run in nearly-linear time. These proof systems can be used for delegating computation: a

Non-Interactive Proofs of Proximity

by Tom Gur, Ron D. Rothblum , 2013
"... We initiate a study of non-interactive proofs of proximity. These proof-systems consist of a verifier that wishes to ascertain the validity of a given statement, using a short (sublinear length) explicitly given proof, and a sublinear number of queries to its input. Since the verifier cannot even re ..."
Abstract - Cited by 6 (1 self) - Add to MetaCart
We initiate a study of non-interactive proofs of proximity. These proof-systems consist of a verifier that wishes to ascertain the validity of a given statement, using a short (sublinear length) explicitly given proof, and a sublinear number of queries to its input. Since the verifier cannot even

A Framework for Interactive Proof

by David Aspinall, Christoph Lüth, Daniel Winterstein
"... Abstract. This paper introduces Proof General Kit, a framework for software components tailored to interactive proof development. The goal of the framework is to enable flexible environments for managing formal proofs across their life-cycle: creation, maintenance and exploitation. The framework con ..."
Abstract - Cited by 13 (2 self) - Add to MetaCart
Abstract. This paper introduces Proof General Kit, a framework for software components tailored to interactive proof development. The goal of the framework is to enable flexible environments for managing formal proofs across their life-cycle: creation, maintenance and exploitation. The framework

Interactive Proof: Applications to Semantics

by Gerwin Klein
"... Abstract. Building on a previous lecture in the summer school, the introduction to interactive proof, this lecture demonstrates a specific application of interactive proof assistants: the semantics of programming languages. In particular, I show how to formalise a small imperative programming langua ..."
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Abstract. Building on a previous lecture in the summer school, the introduction to interactive proof, this lecture demonstrates a specific application of interactive proof assistants: the semantics of programming languages. In particular, I show how to formalise a small imperative programming

On the complexity of space bounded interactive proofs

by Anne Condon, Richard J. Lipton , 2005
"... We prove two results on interactive proof systems with 2-way probabilistic finite state verifiers. The first is a lower bound on the power of such proof systems, if they are not required to halt with high probability on rejected inputs: we show that they can accept any recursively enumerable languag ..."
Abstract - Cited by 78 (5 self) - Add to MetaCart
We prove two results on interactive proof systems with 2-way probabilistic finite state verifiers. The first is a lower bound on the power of such proof systems, if they are not required to halt with high probability on rejected inputs: we show that they can accept any recursively enumerable
Results 1 - 10 of 4,706