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Topic: Interactive proof system

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	Interactive proof system - Wikipedia, the free encyclopedia
		In computational complexity theory, an interactive proof system is an abstract machine that models computation as the exchange of messages between two parties.
		The specific nature of the system, and so the complexity class of languages it can recognize, depends on what sort of bounds are put on the verifier, as well as what abilities it is given — for example, most interactive proof systems depend critically on the verifier's ability to make random choices.
		This strong relationship between a probabilistic interactive protocol and a classical deterministic space-bounded machine gave a concept of the power and the limitations of interactive proof systems and established valuable ties between the two subfields.
	en.wikipedia.org /wiki/Interactive_proof_system (1971 words)

	Encyclopedia: Interactive proof system (Site not responding. Last check: )
		In cryptography, a zero-knowledge proof is an interactive method for one party to prove to another that a (usually mathematical) statement is true, without revealing anything other than the verity of the statement.
		In theoretical computer science, an ordinary (deterministic) Turing machine has a transition rule that specifies for a given current state of the head and computer (s,q) a single instruction (s, q, d), where s is the symbol to be written by the head, q is the subsequent state of...
		Main article: Probabilistically checkable proof In computational complexity theory, PCP is the class of decision problems having probabilistically checkable proof systems.
	www.nationmaster.com /encyclopedia/Interactive-proof-system (3956 words)

	Interactive proof system -- Facts, Info, and Encyclopedia article (Site not responding. Last check: )
		The interactive proof system is a concept in (Click link for more info and facts about computational complexity theory) computational complexity theory that models (Problem solving that involves numbers or quantities) computation as the exchange of messages between two parties.
		This concept of computation as interaction between parties was suggested by Babai et al and (Click link for more info and facts about Goldwasser) Goldwasser et al.
		It has also been proven that the set of all languages recognizable by interaction (which is called IP) is equivalent to (Click link for more info and facts about PSPACE) PSPACE, the set of all languages recognizable by a (A hypothetical computer with an infinitely long memory tape) Turing machine using polynomial space.
	www.absoluteastronomy.com /encyclopedia/i/in/interactive_proof_system.htm (273 words)

	UW-Madison Theory of Computing Seminar 1/29/02 (Site not responding. Last check: )
		Interactive proof systems were first introduced in 1985, both as a natural extension of the class NP and as a model for various cryptographic situations.
		An interactive proof system consists of two interacting parties: a computationally unbounded prover and a polynomial-time verifier.
		Quantum interactive proof systems are interactive proof systems in which the prover and verifier may perform quantum computations and exchange quantum messages.
	www.cs.wisc.edu /areas/theory/Seminar/Spring02/020129.html (129 words)

	12. The Proof System
		If the proof is for mechanical verification only (whether by a digital computer or a human being acting like one), then the criteria of acceptability can be specified unambiguously as a set of rules for determining which sequences of symbols constitute proofs.
		Interactive mode is used for proof discovery and interactive experimentation with new proof techniques.
		All the proof commands and node-movement commands given during the course of a single proof are recorded as a component of the deduction graph.
	imps.mcmaster.ca /manual/node17.html (2416 words)

	Method and system for message delivery utilizing zero knowledge interactive proof protocol - Patent 6011848
		Then, at a point at which the zero knowledge interactive proof protocol is finished normally, it implies that the user authentication according to the zero knowledge interactive proof protocol has been made normally, and besides it becomes a proof for the fact that the user has correctly received the check bits e.sub.jk (j=1, 2,.
		Also, it becomes a system in which the execution of the protocol is immediately discontinued when it is detected as the illegal user, such that it is possible to eliminate a case in which the illegal user illegally obtains the requested message.
		Also, it becomes a system which is made such that, by a neutral arbitration organization such as a court, it is possible to check the authenticity of the log as a valid evidence, and judge which one of a claim of the information provider and a claim of the user is a proper one.
	www.freepatentsonline.com /6011848.html (12299 words)

	Encyclopedia: Probabilistically checkable proof (Site not responding. Last check: )
		In this process a correct proof will always be declared as such, while any attempt to prove a wrong statement will be declared false with probability at least 1/2 (repeating this process several times can detect a false proof with arbitrarily high probability).
		In complexity theory, a PCP system can be viewed as an interactive proof system in which the prover is a memoryless oracle (essentially a string) and the verifier is a polynomial-time randomized algorithm.
		For an input which belongs to the language (a YES-instance), there exists an oracle (or proof) for which the verifier accepts with certainty; for NO-instances, the verifier rejects with probability at least 1/2, whatever be the oracle (compare Co-RP).
	www.nationmaster.com /encyclopedia/Probabilistically-checkable-proof (496 words)

	[No title] (Site not responding. Last check: )
		Proof: Proof is a fixed sequence consisting of statements that are either self evident or are derived from previous statements via self-evident rules.
		Interactive proof systems: Interactive proof systems refers to two computational tasks: Producing a proof and verifying the validity of the proof.
		The party produing the proof is called the prover (P) and the party verifying the proof is called the verified (V).
	www.cs.rit.edu /~svc5135/notes.txt (287 words)

	Method and system for message delivery utilizing zero knowledge interactive proof protocol - Patent 6044463 (Site not responding. Last check: )
		The message delivery system as described in claim 3, wherein the information provider terminal also includes an information provider secret information storage unit for storing an information to be kept in secret by the information provider which is to be utilized by the cryptosystem unit in carrying out the secret communication.
		The message delivery system as described in claim 7, wherein the arbitration terminal also has a verification unit for verifying whether a signature of a signed work key in the log data is authentic.
		Then, at a point at which the zero knowledge interactive proof protocol is finished normally, it implies that the user authentication according to the zero knowledge interactive proof protocol has been made normally, and besides it becomes proof that the user has normally received the check bits ei (i=1, 2,.
	www.freepatentsonline.com /6044463.html (13206 words)

	Mechanized Reasoning Systems (Site not responding. Last check: )
		IMPS -- is an interactive proof system based on a nonconstructive version of simple type theory with partial functions and subtypes, with a theory interpetation mechanism.
		NUPRL is a proof system for an intuitionistic type theory based on Martin Lof type theory, with proof by refinement and extraction of programs from proofs.
		WinKE is an interactive theorem proving assistant based on the KE calculus, developed to support teaching logic and reasoning to undergraduates.
	www-formal.stanford.edu /clt/ARS/systems.html (1545 words)

	An Interactive Proof System for Map Theory (Site not responding. Last check: )
		We have developed an interactive proof system for Map Theory using the generic theorem prover Isabelle.
		Within the system, we have formalized the development of ZFC from first principles, as well as a non-trivial part of elementary number theory, allowing us to prove that the rationals are linearly ordered field.
		The dissertation describes the proof techniques used, and in particular describes the type system developed to facilitate typed rewriting in a fundamentally untyped logic.
	www.mangust.dk /skalberg/phd (115 words)

	NEXPTIME (Site not responding. Last check: )
		NEXPTIME often arises in the context of interactive proof systems, where there are two major characterizations of it.
		The first is the MIP proof system, where we have two all-powerful provers which communicate with a randomized polynomial-time verifier (but not with each other).
		Another interactive proof system characterizing NEXPTIME is a certain class of probabilistically checkable proofs.
	www.worldhistory.com /wiki/N/NEXPTIME.htm (474 words)

	How to construct zero-knowledge proof systems for NP (Site not responding. Last check: )
		Zero-knowledge proofs are probabilistic and interactive proofs that efficiently demonstrate membership in the language without conveying any additional knowledge.
		The wide applicability of zero-knowledge was demonstrated in Proofs that Yield Nothing But their Validity or All Languages in NP have Zero-Knowledge Proofs, coauthored by Goldreich, Micali and Wigderson [JACM, July 1991].
		All previously known zero-knowledge proofs were for sets related to number theory, and furthermore GNI was the first set not known to be in NP that was shown to have an interactive proof system.
	www.wisdom.weizmann.ac.il /~oded/gmw1.html (246 words)

	LEGO Proof Development System: User's Manual
		LEGO is an interactive proof development system (proof checker) designed and implemented by R. Pollack in Edinburgh.
		An overview of the basic theory and implementation of LEGO may be found in [Pol88], where most of the features of the system are sketched and explained, and a simple and informal introduction to the system can be found in [Bur89b].
		LEGO is a powerful tool for interactive proof development in the natural deduction style.
	www.lfcs.inf.ed.ac.uk /reports/92/ECS-LFCS-92-211 (409 words)

	Interactive Proof Systems
		It is fed into the system on an input tape, which is readable by both P and V. P and V take turns to be active.
		The difference between a deterministic interactive proof system (DIP) and an interactive proof system (IP) is that the verifier V in IP is now a probabilistic Turing machine with a polynomial time bound.
		It is conjectured that GNI is not in NP.
	www2.hawaii.edu /~hmauch/subdir2/IPSystemsnew.htm (1856 words)

	IMPS Home Page
		IMPS is an Interactive Mathematical Proof System intended to provide organizational and computational support for the traditional techniques of mathematical reasoning.
		The system consists of a database of mathematics (represented as a network of axiomatic theories linked by theory interpretations) and a collection of tools for exploring, applying, extending, and communicating the mathematics in the database.
		In contrast to the formal proofs described in logic textbooks, IMPS proofs are a blend of computation and high-level inference.
	imps.mcmaster.ca (524 words)

	CIS: Zero-Knowledge Proofs
		Zero-knowledge proofs were introduced by Goldwasser, Micali and Rackoff in The Knowledge Complexity of Interactive Proof Systems (SIAM J. of Comuting, January 1989).
		Concurrent executions of a zero-knowledge protocol by a single prover (with one or more verifiers) may leak information and may not be zero-knowledge in toto; for example, in the case of zero-knowledge interactive proofs or arguments, the interactions remain proofs but may fail to remain zero-knowledge.
		An interactive proof system (or argument) (P,V) is concurrent zero-knowledge if whenever the prover engages in polynomially many concurrent executions of (P,V), with (possibly distinct) colluding polynomial time bounded verifiers V1,..., V{poly(n)}, the entire undertaking is zero-knowledge.
	theory.lcs.mit.edu /~cis/zk/zk.html (1271 words)

	DECLARE: A Prototype Declarative Proof System for Higher Order Logic
		The purpose of DECLARE is to explore mechanisms of specification and proof that may be incorporated into toher theorem provers.
		Proofs in DECLARE are expressed as proof outlines, in a language that approximates written mathematics.
		The system includes an abstract/article mechanism that provides a way of isolating the process of formalization from what results, and simultaneously allow the efficient separate processing of work units.
	research.microsoft.com /pubs/view.aspx?pubid=435 (156 words)

	Adding Critics to the IsaPlanner Proof Planning System (Site not responding. Last check: )
		Proof planning is a technique for the automatic guidance of mechanical theorem provers.
		Proof planning includes "critics": variations of tactics which critique and patch a failing proof attempt.
		This kind of proof patching is usually thought to require human intervention and its automation is a considerable advance.
	www.inf.ed.ac.uk /teaching/courses/diss/props/028_bundy13.html (348 words)

	Elements of Hypermedia Design - 27.1 Components of the Proof Visualization System (Site not responding. Last check: )
		The lack of previous work in this area is partly due to the fact that proofs often involve hypothetical and abstract objects created for the purpose of the proof.
		Though our system could be stand-alone, we suggest that it be used in conjunction with the following parts: (a) a proof orientation (introduction) describing the problem and the algorithm through pseudocode that explains the important steps, and (b) an integrated animation of the algorithm.
		The proof visualization is controlled by the proof-dialog: A sequence of statements is presented to the users and they can either accept them or ask for more explanation of any of these statements.
	www.ickn.org /elements/hyper/cyb120.htm (521 words)

	Notational Definition and Top-Down Refinement for Interactive Proof Development Systems, by Timothy G. Griffin (Site not responding. Last check: )
		This thesis is concerned with issues related to the design and implementation of systems that support interactive proof development.
		The implementation of mechanisms that support notational definitions in interactive proof development systems as well as applications to Nuprl are discussed.
		Rather than presenting, as is done for Nuprl, refinement and refinement rules as primitive notions that are extended by grafting on tactics, tactics are instead viewed as the basic notion from which refinement trees arise as tree-structured representations of the iterated composition of tactics.
	www.nuprl.org /documents/Griffin/NotationalDefinition.html (351 words)

	Dwork Abstract (Site not responding. Last check: )
		A zero-knowledge interactive proof system allows a prover to convince a verifier of the truth of a statement, without revealing any additional information about "why" the statement is true.
		Determining the minimum amount of interaction needed for zero-knowledge proofs has been the subject of intensive study since the concept was introduced in 1985 by Goldwasser, Micali, and Rackoff.
		Consider a setting in which the prover enters a special proving chamber from which access to the outside world is impossible and into which only a certain amount of information, or advice, may be carried.
	www.cis.upenn.edu /~colloq/abstracts-2001/dwork.html (126 words)

	Bateman/Zock: NLG list system entry: P.rex
		P.rex is an interactive proof explanation system that adapts its explanations to the user and flexibly reacts to his questions or requests.
		As a generic system, P.rex can be connected to different theorem provers, namely by means of the formal language TWEGA for specifying proofs and mathematical theories.
		A proof of a theorem can be represented hierarchically in TWEGA such that the various levels of abstraction are made explicit.
	www.fb10.uni-bremen.de /anglistik/langpro/NLG-table/details/P.rex.htm (320 words)

	[No title] (Site not responding. Last check: )
		[ TGIF talk abstract ] "PSPACE has constant round quantum interactive proof systems" John Watrous Presented by Daniel Preda 10/17/2003 In this paper we consider quantum interactive proof systems, i.e., interactive proof systems in which the prover and verifier may perform quantum computations and exchange quantum messages.
		It is proved that every language in PSPACE has a quantum interactive proof system that requires only three messages to be sent between the prover and verifier, while having exponentially small (one-sided) probability of error.
		It follows that quantum interactive proof systems are strictly more powerful than classical interactive proof systems in the constant-round case unless the polynomial time hierarchy collapses to the second level.
	www.cs.berkeley.edu /~alexf/tgif/tgif-1017.txt (112 words)

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