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The knowledge complexity of interactive proof systems
 in Proc. 27th Annual Symposium on Foundations of Computer Science
, 1985
"... Abstract. 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/nonHamiltoni ..."
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Cited by 1086 (41 self)
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Abstract. 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 this paper a computational complexity theory of the "knowledge " contained in a proof is developed. Zeroknowledge proofs are defined as those proofs that convey no additional knowledge other than the correctness of the proposition in question. Examples of zeroknowledge proof systems are given for the languages of quadratic residuosity and quadratic nonresiduosity. These are the first examples of zeroknowledge proofs for languages not known to be efficiently recognizable. Key words, cryptography, zero knowledge, interactive proofs, quadratic residues AMS(MOS) subject classifications. 68Q15, 94A60 1. Introduction. It is often regarded that saying a language L is in NP (that is, acceptable in nondeterministic polynomial time) is equivalent to saying that there is a polynomial time "proof system " for L. The proof system we have in mind is one where on input x, a "prover " creates a string a, and the "verifier " then computes on x and a in time polynomial in the length of the binary representation of x to check that
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 312 (29 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) and that MIP=NEXP (Babai, Fortnow and Lund).
Trading Group Theory for Randomness
, 1985
"... In a previous paper [BS] we proved, using the elements of the Clwory of nilyotenf yroupu, that some of the /undamcnla1 computational problems in mat & proup, belong to NP. These problems were also ahown to belong to CONP, assuming an unproven hypofhedi.9 concerning finilc simple Q ’ oup,. The a ..."
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Cited by 304 (9 self)
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In a previous paper [BS] we proved, using the elements of the Clwory of nilyotenf yroupu, that some of the /undamcnla1 computational problems in mat & proup, belong to NP. These problems were also ahown to belong to CONP, assuming an unproven hypofhedi.9 concerning finilc simple Q ’ oup,. The aim of this paper is t.o replace most of the (proven and unproven) group theory of IBS] by elementary combinatorial argumenls. The rev & we prove is that relative to a random oracle f3, tbc meutioned matrix group problems belong to (NPncoNP)L! Thr problems we consider arr membership in and order of a matrix group given by a list of gnrrntors. These probtrms can bc vicwrd as m~lt~idimcnsio~r;lI vemiorm of a closr rrldivr of t.hc disrrct,r logarilhm prob1c.m. I tencc A’ltiro.VI ’ might be the lowrst natural romplcxity rla.us t bry may ii1 in. Wr remark that the resutt,s remain valid for blark boz groupa where group operations are prrformcd by an oracle. Thcb tools we inlroduce seem interesting in their own right. \Ve define a new hierarchy of complexit)y ctesscs A.4Ak) “just above NP’, introduring Arthur ud. Merlin games, the bonndedaway version of Pnpadimitriou’s Games against Nature. We prove th:rt. in spite of their analogy with the polynomial time hierarchy, the finite levrls of this hierarchy collapse t,o Afsf=Ah42). Using a combinatorial lemma on finite groups [IIE], we construct a game by whirh t.he nondeterministic player (Merlin) is able to coavlnre the random player (Arthur) about the rctation ICj=N provided Arthur trusts conclusions based on st,atisticnl rvidrnce (such as a SolovayStrassen type “proof” of primatit,y). One can prove that AM consists precisely of t&ose langungrs which belong to iV @ for almost every oracle 13. Our hirrarchy has an intrrcsjdng, still unclarified retation to imother hierarchy, obt,ained by rcnloving the cent.rat ingrrdirnt from the l&r ~a. Ezpcrl games of Goldwasser, Micali and Rackoff.
The NPcompleteness column: an ongoing guide
 Journal of Algorithms
, 1985
"... This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & ..."
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Cited by 196 (0 self)
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This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co., New York, 1979 (hereinafter referred to as ‘‘[G&J]’’; previous columns will be referred to by their dates). A background equivalent to that provided by [G&J] is assumed, and, when appropriate, crossreferences will be given to that book and the list of problems (NPcomplete and harder) presented there. Readers who have results they would like mentioned (NPhardness, PSPACEhardness, polynomialtimesolvability, etc.) or open problems they would like publicized, should
The Complexity of Stochastic Games
 Information and Computation
, 1992
"... We consider the complexity of stochastic games  simple games of chance played by two players. We show that the problem of deciding which player has the greatest chance of winning the game is in the class NP " coNP. 1 Introduction We consider the complexity of a natural combinatorial problem ..."
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Cited by 161 (2 self)
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We consider the complexity of stochastic games  simple games of chance played by two players. We show that the problem of deciding which player has the greatest chance of winning the game is in the class NP " coNP. 1 Introduction We consider the complexity of a natural combinatorial problem, that of deciding the outcome of a special kind of stochastic game. A simple stochastic game (SSG) is a directed graph with three types of vertices, called max, min and average vertices. There is a special start vertex and two special sink vertices, called the 0sink and the 1sink. For simplicity, we assume that all vertices have exactly two (not necessarily distinct) neighbors, except for the sink vertices, which have no neighbors. The graph models a game between two players, 0 and 1. In the game, a token is initially placed on the start vertex, and at each step of the game the token is moved from a vertex to one of its neighbors, according to the following rules: At a min vertex, player 0 cho...
Universal Voting Protocol Tweaks to Make Manipulation Hard
, 2003
"... Voting is a general method for preference aggregation in multiagent settings, but seminal results have shown that all (nondictatorial) voting protocols are manipulable. One could try to avoid manipulation by using voting protocols where determining a beneficial manipulation is hard computationa ..."
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Cited by 109 (27 self)
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Voting is a general method for preference aggregation in multiagent settings, but seminal results have shown that all (nondictatorial) voting protocols are manipulable. One could try to avoid manipulation by using voting protocols where determining a beneficial manipulation is hard computationally.
Vote Elicitation: Complexity and StrategyProofness
, 2002
"... significant attention in singleagent settings. It is also a key problem in multiagent systems, but has received little attention here so far. In this setting, the agents may have different preferences that often must be aggregated using voting. ..."
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Cited by 81 (21 self)
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significant attention in singleagent settings. It is also a key problem in multiagent systems, but has received little attention here so far. In this setting, the agents may have different preferences that often must be aggregated using voting.
Sound and efficient closedworld reasoning for planning
 Artificial Intelligence
, 1997
"... Closedworld inference is the process of determining that a logical sentence is false based on its absence from a knowledge base, or the inability to derive it. This process is essential for planning with incomplete information. We describe a novel method for closedworld inference and update over t ..."
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Cited by 79 (12 self)
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Closedworld inference is the process of determining that a logical sentence is false based on its absence from a knowledge base, or the inability to derive it. This process is essential for planning with incomplete information. We describe a novel method for closedworld inference and update over the firstorder theories of action used by planning algorithms such as NONLIN, TWEAK, and UCPOP. We show the method to be sound and efficient, but incomplete. In our experiments, closedworld inference consistently averaged about 2 milliseconds, while updates averaged approximately 1.2 milliseconds. We incorporated the method into the XII planner, which supports our Internet Softbot (software robot). The method cut the number of actions executed by the Softbot bya factor of one hundred, and resulted in a corresponding speedup to XII. 1
The Complexity Of Optimal Queueing Network Control
 Mathematics of Operations Research
, 1994
"... : We show that several wellknown optimization problems related to the optimal control of queues are provably intractable independently of any unproven conjecture such as P6=NP. In particular, we show that several versions of the problem of optimally controlling a simple network of queues with si ..."
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Cited by 69 (2 self)
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: We show that several wellknown optimization problems related to the optimal control of queues are provably intractable independently of any unproven conjecture such as P6=NP. In particular, we show that several versions of the problem of optimally controlling a simple network of queues with simple arrival and service distributions and multiple customer classes is complete for exponential time. This is perhaps the first such intractability result for a wellknown optimization problem. We also show that the restless bandit problem (the generalization of the multiarmed bandit problem to the case in which the unselected processes are not quiescent) is complete for polynomial space. 1. INTRODUCTION The optimal control of a network of queues is a wellknown, much studied, and notoriously difficult problem. We are given several servers, a set of customer classes, and classdependent probability distributions for the service times. For each customer class, there is only one server tha...
Contingent Planning Under Uncertainty via Stochastic Satisfiability
 Artificial Intelligence
, 1999
"... We describe two new probabilistic planning techniques cmaxplan and zanderthat generate contingent plans in probabilistic propositional domains. Both operate by transforming the planning problem into a stochastic satisfiability problem and solving that problem instead. cmaxplan encodes t ..."
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Cited by 63 (10 self)
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We describe two new probabilistic planning techniques cmaxplan and zanderthat generate contingent plans in probabilistic propositional domains. Both operate by transforming the planning problem into a stochastic satisfiability problem and solving that problem instead. cmaxplan encodes the problem as an EMajsat instance, while zander encodes the problem as an SSat instance. Although SSat problems are in a higher complexity class than EMajsat problems, the problem encodings produced by zander are substantially more compact and appear to be easier to solve than the corresponding EMajsat encodings. Preliminary results for zander indicate that it is competitive with existing planners on a variety of problems. Introduction When planning under uncertainty, any information about the state of the world is precious. A contingent plan is one that can make action choices contingent on such information. In this paper, we present an implemented framework for contingent pl...