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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 1058 (39 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
Belief, awareness, and limited reasoning
 ARTIFICIAL INTELLIGENCE
, 1988
"... Several new logics for belief and knowledge are introduced and studied, all of which have the property that agents are not logically omniscient. In particular, in these logics, the set of beliefs of an agent does not necessarily contain all valid formulas. Thus, these logics are more suitable than t ..."
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Cited by 124 (12 self)
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Several new logics for belief and knowledge are introduced and studied, all of which have the property that agents are not logically omniscient. In particular, in these logics, the set of beliefs of an agent does not necessarily contain all valid formulas. Thus, these logics are more suitable than traditional logics for modelling beliefs of humans (or machines) with limited reasoning capabilities. Our first logic is essentially an extension of Levesque's logic of implicit and explicit belief, where we extend to allow multiple agents and higherlevel belief (i.e., beliefs about beliefs). Our second logic deals explicitly with "awareness," where, roughly speaking, it is necessary to be aware of a concept before one can have beliefs about it. Our third logic gives a model of "local reasoning," where an agent is viewed as a "society of minds," each with its own cluster of beliefs, which may contradict each other.
Model Checking vs. Theorem Proving: A Manifesto
, 1991
"... We argue that rather than representing an agent's knowledge as a collection of formulas, and then doing theorem proving to see if a given formula follows from an agent's knowledge base, it may be more useful to represent this knowledge by a semantic model, and then do model checking to se ..."
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Cited by 117 (5 self)
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We argue that rather than representing an agent's knowledge as a collection of formulas, and then doing theorem proving to see if a given formula follows from an agent's knowledge base, it may be more useful to represent this knowledge by a semantic model, and then do model checking to see if the given formula is true in that model. We discuss how to construct a model that represents an agent's knowledge in a number of different contexts, and then consider how to approach the modelchecking problem.
Reasoning about Information Change
, 1997
"... In this paper, we have combined techniques from epistemic and dynamic logic to arrive at a logic for describing multiagent information change. The key concept of dynamic semantics is that the meaning of an assertion is the way in which the assertion changes the information of the hearer. Thus a dyn ..."
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Cited by 100 (4 self)
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In this paper, we have combined techniques from epistemic and dynamic logic to arrive at a logic for describing multiagent information change. The key concept of dynamic semantics is that the meaning of an assertion is the way in which the assertion changes the information of the hearer. Thus a dynamic epistemic semantics consist in a explicit formal definition of the information change potential of a sentence. We used these ideas to arrive at the system of Dynamic Epistemic Semantics, which is semantics for a language describing information change in a multiagent setting. This semantics proved useful for analyzing the Muddy Children paradox, and also for giving a semantics for knowledge programs, since it enabled us to model knowledge change by giving an explicit semantics to the triggers of the information change (the latter being the assertions made, or the messages sent). We feel that this is an important extension, since standard approaches to for example the Muddy Children (e.g. Fagin et al. 1995) generally use static epistemic logics like S5 to describe the situation before and after a certain epistemic event, leaving the transition between `before' and `after' to considerations in the metalanguage.
A Rigorous, Operational Formalization of Recursive Modeling
, 1995
"... We present a formalization of the Recursive Modeling Method, which we have previously, somewhat informally, proposed as a method that autonomous artificial agents can use for intelligent coordination and communication with other agents. Our formalism is closely related to models proposed in the area ..."
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Cited by 74 (15 self)
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We present a formalization of the Recursive Modeling Method, which we have previously, somewhat informally, proposed as a method that autonomous artificial agents can use for intelligent coordination and communication with other agents. Our formalism is closely related to models proposed in the area of game theory, but contains new elements that lead to a different solution concept. The advantage of our solution method is that always yields the optimal solution, which is the rational action of the agent in a multiagent environment, given the agent's state of knowledge and its preferences, and that it works in realistic cases when agents have only a finite amount of information about the agents they interact with. Introduction Since its initial conceptual development several years ago (Gmytrasiewicz, Durfee, & Wehe 1991a; 1991b), the Recursive Modeling Method (RMM) has provided a powerful decisiontheoretic underpinning for coordination and communication decisionmaking, including dec...
Complete Axiomatizations for Reasoning about Knowledge and Time
 STUDIA LOGICA
, 1999
"... Sound and complete axiomatizations are provided for a number of different logics involving modalities for knowledge and time. These logics arise from different choices for various parameters regarding the regarding the interaction of knowledge with time and regarding the language used. All the logic ..."
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Cited by 65 (6 self)
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Sound and complete axiomatizations are provided for a number of different logics involving modalities for knowledge and time. These logics arise from different choices for various parameters regarding the regarding the interaction of knowledge with time and regarding the language used. All the logics considered involve the discrete time linear temporal logic operators `next' and `until' and an operator for the knowledge of each of a number of agents. Both the single agent and multiple agent cases are studied: in some instances of the latter there is also an operator for the common knowledge of the group of all agents. Four different semantic properties of agents are considered: whether they have a unique initial state, whether they operate synchronously, whether they have perfect recall, and whether they learn. The property of no learning is essentially dual to perfect recall. Not all settings of these parameters lead to recursively axiomatizable logics, but sound and complete axiomatizations are presented for all the ones that do.
Reasoning about knowledge: An overview
 Proceedings of the 1986 Conference on Theoretical Aspects of Reasoning About Knowledge
, 1986
"... Abstract: In this overview paper, I will attempt to identify and describe some of the common threads that tie together work in reasoning about knowledge in such diverse fields as philosophy, economics, linguistics, artificial intelligence, and theoretical computer sciencce. I will briefly discuss so ..."
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Cited by 31 (3 self)
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Abstract: In this overview paper, I will attempt to identify and describe some of the common threads that tie together work in reasoning about knowledge in such diverse fields as philosophy, economics, linguistics, artificial intelligence, and theoretical computer sciencce. I will briefly discuss some of the more recent work, particularly in computer science, and suggest some lines for future research.
A Theory Of Knowledge And Ignorance For Many Agents
 Journal of Logic and Computation
, 1993
"... We extend the notion of "only knowing" introduced by Halpern and Moses [11] to many agents and to a number of modal logics. In this approach, "all an agent knows is ff" is true in a structure M if, in M , the agent knows ff and has a maximum set of "possibilities". To e ..."
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Cited by 25 (4 self)
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We extend the notion of "only knowing" introduced by Halpern and Moses [11] to many agents and to a number of modal logics. In this approach, "all an agent knows is ff" is true in a structure M if, in M , the agent knows ff and has a maximum set of "possibilities". To extend this approach, we need to make precise what counts as a "possibility". In the singleagent case, we can identify a possibility with a truth assignment. In the multiagent case, things are more complicated. We consider three notions of possibility (all related). We argue that the first is most appropriate for nonintrospective logics, such as Kn , Tn , and S4n , the second is most appropriate for K45n and KD45n , and the last is most appropriate for S5n . With the appropriate notion of possibility, we show that are reasonable extensions in all cases. Our results also shed light on the singleagent case. It was always assumed that one of the key aspects of HalpernMoses approach in the singleagent case was its use o...
The wakeup problem
 SIAM Journal on Computing
, 1996
"... We study a new problem, the wakeup problem, that seems to be fundamental in distributed computing. We present efficient solutions to the problem and show how these solutions can be used to solve the consensus problem, the leader election problem, and other related problems. The main question we try ..."
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Cited by 24 (5 self)
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We study a new problem, the wakeup problem, that seems to be fundamental in distributed computing. We present efficient solutions to the problem and show how these solutions can be used to solve the consensus problem, the leader election problem, and other related problems. The main question we try to answer is, how much memory is needed to solve the wakeup problem? We assume a model that captures important properties of real systems that have been largely ignored by previous work on cooperative problems.
Common Knowledge and Update in Finite Environments
 Information and Computation
, 1997
"... Logics of knowledge have been shown to provide a useful approach to the high level specification and analysis of distributed systems. It has been proposed that such systems can be developed using knowledgebased protocols, in which agents' actions have preconditions that test their state of kno ..."
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Cited by 20 (5 self)
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Logics of knowledge have been shown to provide a useful approach to the high level specification and analysis of distributed systems. It has been proposed that such systems can be developed using knowledgebased protocols, in which agents' actions have preconditions that test their state of knowledge. Both computerassisted analysis of the knowledge properties of systems and automated compilation of knowledgebased protocols require the development of algorithms for the computation of states of knowledge. This paper studies one of the computational problems of interest, the model checking problem for knowledge formulae in the S5 n Kripke structures generated by finite state environments in which states determine an observation for each agent. Agents are assumed to have perfect recall, and may operate synchronously or asynchronously. It is shown that, in this setting, model checking of common knowledge formulae is intractable, but efficient incremental algorithms are developed for formu...