## Knowledge, probability, and adversaries (1993)

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Venue: | Journal of the ACM |

Citations: | 76 - 24 self |

### BibTeX

@ARTICLE{Halpern93knowledge,probability,,

author = {Joseph Y. Halpern and Mark R. Tuttle},

title = {Knowledge, probability, and adversaries},

journal = {Journal of the ACM},

year = {1993},

pages = {917--962}

}

### Years of Citing Articles

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### Abstract

Abstract: What should it mean for an agent toknowor believe an assertion is true with probability:99? Di erent papers [FH88, FZ88a, HMT88] givedi erent answers, choosing to use quite di erent probability spaces when computing the probability that an agent assigns to an event. We showthat each choice can be understood in terms of a betting game. This betting game itself can be understood in terms of three types of adversaries in uencing three di erent aspects of the game. The rst selects the outcome of all nondeterministic choices in the system� the second represents the knowledge of the agent's opponent in the betting game (this is the key place the papers mentioned above di er) � the third is needed in asynchronous systems to choose the time the bet is placed. We illustrate the need for considering all three types of adversaries with a number of examples. Given a class of adversaries, we show howto assign probability spaces to agents in a way most appropriate for that class, where \most appropriate " is made precise in terms of this betting game. We conclude by showing how di erent assignments of probability spaces (corresponding to di erent opponents) yield di erent levels of guarantees in probabilistic coordinated attack.

### Citations

1086 | The Knowledge Complexity of Interactive Proof Systems
- Goldwasser, Micali, et al.
- 1985
(Show Context)
Citation Context ...ack. It may be worth reconsidering a number of algorithms to see if they can be redesigned to give stronger guarantees. This may be particularly appropriate in the context of zero-knowledge protocols =-=[GMR89]-=-, where the current definitions allow a prover to continue playing against a verifier even when the prover knows perfectly well that it has already leaked information to the verifier, and may continue... |

520 | Knowledge and common knowledge in a distributed environment
- Halpern, Moses
- 1990
(Show Context)
Citation Context ...s, and in later sections we will vary the probability distributions associated with these runs. Our model is actually the model given in [HF89], which is itself a simplification of the model given in =-=[HM90]-=-. Both models are heavily influenced by models for distributed computation. Consider an arbitrary system of n interacting agents p 1 ; : : : ; p n . Intuitively, a run of a system is a complete descri... |

443 |
Agreeing to Disagree
- Aumann
- 1976
(Show Context)
Citation Context ...t with di erent odds. Suppose we continue in this fashion until nally pj o ers pi a bet with odds that pi accepts, and pj no longer changes his mind. A well-known result of game theory, due to Aumann =-=[Aum76]-=-, says that at this point both pi and pj must agree that the probability of' is exactly 1= . Roughly speaking, this says that rational agents cannot agree to disagree. 21 Acknowledgments Thanks to Mos... |

374 |
A guide to completeness and complexity for modal logics of knowledge and belief
- Halpern, Moses
- 1992
(Show Context)
Citation Context ...define ' is common knowledge to G, denoted CG', by CG' j EG'sEGEG's\Delta \Delta \DeltasE m G 's\Delta \Delta \Delta : It is not hard to prove that common knowledge satisfies the following statements =-=[HM92]-=-: 1. the fixed point axiom: CG' j EG ('sCG'): 2. the induction rule: ?From / oe EG (/s') infer / oe CG ': The first statement says that CG' is a fixed point of the equation X j EG ('sX). It can be sho... |

296 |
Notes on database operating systems
- GRAY
- 1978
(Show Context)
Citation Context ...t analyses of a protocol. The purpose of this section is to make clear the distinction between distributions over runs and distributions over points. To begin, consider the Coordinated Attack problem =-=[Gra78]-=-. Two generals A and B must decide whether to attack a common enemy, but we require that any attack be a coordinated attack; that is, A attacks iff B attacks. Unfortunately, they can communicate only ... |

237 | Automatic verification of probabilistic concurrent finite-state programs - Vardi - 1985 |

230 | A Logic for Reasoning about Probabilities - Fagin, Halpern, et al. - 1990 |

198 |
Probabilistic algorithm for testing primality
- Rabin
- 1980
(Show Context)
Citation Context ...want to assume a probability distribution on the inputs. We want to know that for each choice of input, the algorithm gives the right answer with high probability. Rabin's primality-testing algorithm =-=[Rab80]-=- is based on the existence of a polynomial-time computable predicate P n (a) with the following properties: (1) if n is composite, then at least 3=4 of the a 2 f1; : : : ; n \Gamma 1g cause P n (a) to... |

163 | Reasoning about knowledge and probability
- Fagin, Halpern
- 1994
(Show Context)
Citation Context ...algorithm would almost certainly have found a witness had n been composite. A number of recent papers have tried to formalize this sort of reasoning about knowledge and probability. Fagin and Halpern =-=[FH94]-=- present an abstract model for knowledge and probability in which they assign to each agent-state pair a probability space to be used when computing the probability, according to that agent at that st... |

156 |
The complexity of reasoning about knowledge and time. I. lower bounds
- Halpern, Vardi
- 1989
(Show Context)
Citation Context ... appropriate probability assignments in completely synchronous systems. Intuitively, a system is synchronous if all agents effectively have access to a global clock. Formally, a system is synchronous =-=[HV89]-=- if for all points (r; k) and (r 0 ; k 0 ) and all agents p i , if r i (k) = r 0 i (k 0 ) then k = k 0 . This means, for example, that no two points an agent p i considers indistinguishable can lie on... |

141 |
Girshick, Theory of games and statistical decisions
- Blackwell, A
- 1954
(Show Context)
Citation Context ... of opponent is to assume you are playing against someone whose knowledge is identical to your own. This is what decision theorists implicitly do when talking about an agent's posterior probabilities =-=[BG54]-=-; it is also how we can understand the choice of probability space made in [FZ88a]. By way of contrast, the choice in [HMT88] corresponds to playing someone who has complete knowledge about the past a... |

118 | A Subjectivist’s Guide to Objective Chance - Lewis - 1980 |

88 | Modelling knowledge and action in distributed systems
- Halpern, Fagin
- 1989
(Show Context)
Citation Context ...s section, we fix a model of computation that defines these runs, and in later sections we will vary the probability distributions associated with these runs. Our model is actually the model given in =-=[HF89]-=-, which is itself a simplification of the model given in [HM90]. Both models are heavily influenced by models for distributed computation. Consider an arbitrary system of n interacting agents p 1 ; : ... |

74 |
Allocations of probability
- Shafer
- 1979
(Show Context)
Citation Context ...quite natural to assume, as we do, that all agents in a system follow some kind of a protocol, protocols are not quite so standard in the probability theory literature. Interestingly, Shafer observes =-=[Sha85] that it i-=-s necessary for us to think in terms of protocols if we are to make sense of "conditioning on everything an agent knows" as is done by P post . His argument, which we reproduce here, is base... |

33 |
Is the moon there when nobody looks? Reality and the quantum theory
- Mermin
- 1985
(Show Context)
Citation Context ...know which). This point of view appears in a number of papers in the philosophical literature (for example, [Fra80, Lew80]). Interestingly, this issue even has implications for quantum mechanics (see =-=[Mer85]-=-). We claim that these two choices of probability are best explained in terms of an adversary. This point comes out clearly if we consider betting games. If an agent believes an event E has probabilit... |

32 | A fast Monte Carlo test for primality - Solovay, Strassen - 1977 |

30 | N -process mutual exclusion with bounded waiting by 4 log N shared variables - Rabin - 1982 |

26 | Foundations of knowledge for distributed systems - Fischer, Immerman - 1986 |

26 | A knowledge-based analysis of zero knowledge
- Halpern, Moses, et al.
- 1988
(Show Context)
Citation Context ...be reasonable, they do not tell us how to make this choice. One particular (and quite natural) choice is made in [FZ88a] and some arguments are presented for its appropriateness; 2 another is made in =-=[HMT88]-=- and used to analyze interactive proof systems. It is not initially clear, however, which choice is most appropriate. In this paper, we clarify the issues involved in choosing the right assignment of ... |

24 |
The knowledge complexity ofinteractive proofs
- Goldwasser, Micali, et al.
- 1989
(Show Context)
Citation Context ...tack. It may beworth reconsidering a number of algorithms to see if they can be redesigned to give stronger guarantees. This may be particularly appropriate in the context of zero-knowledge protocols =-=[GMR89]-=-, where the current de nitions allow a prover to continue playing against a veri er even when the prover knows perfectly well that it has already leaked information to the veri er, and may continue to... |

23 | Concurrent common knowledge: defining agreement for asynchronous systems - Panangaden, Taylor - 1992 |

12 |
Reasoning about uncertainty in fault-tolerant distributed systems
- Fischer, Zuck
- 1988
(Show Context)
Citation Context ...his assignment of probability spaces. Although they show that more than one choice may be reasonable, they do not tell us how to make this choice. One particular (and quite natural) choice is made in =-=[FZ88a]-=- and some arguments are presented for its appropriateness; 2 another is made in [HMT88] and used to analyze interactive proof systems. It is not initially clear, however, which choice is most appropri... |

12 | Reasoning about knowledge and probability: preliminary report
- Fagin, Halpern
- 1988
(Show Context)
Citation Context ...d to formalize reasoning about knowledge and probability in such systems. The intent, in part, is to provide a framework within which these guarantees can be described and analyzed. Fagin and Halpern =-=[FH88]-=- present an abstract model for knowledge and probability inwhich they assign to each agentandeach state a probability space to be used when computing the probability, according to that agent at that s... |

10 |
Reasoning about time and chance
- Lehmann, Shelah
- 1982
(Show Context)
Citation Context ...le space assignment that assigns Pref i;c to p i at c, and let P fut denote the probability assignment induced by S fut . We remark that this is the probability assignment used in [HMT88], as well as =-=[LS82]-=-. In the probability space P fut i;c , any event whose outcome has already been determined before reaching the point c will have probability either 0 or 1. Future events (that get decided further down... |

9 | Automatic veri cation of probabilistic concurrent nite-state programs - Vardi - 1985 |

4 |
Puzzle or paradox
- Freund
- 1965
(Show Context)
Citation Context ...erms of protocols if we are to make sense of "conditioning on everything an agent knows" as is done by P post . His argument, which we reproduce here, is based on Freund's puzzle of the two =-=aces (see [Fre65]-=-; other references are given in [Sha85]). Consider a deck with four cards, the ace and deuce of hearts and spades. After a fair shuffle of the deck, two cards are dealt to p 1 . Now what is the probab... |

4 | Concurrent common knowledge: A new de nition of agreement for asynchronous systems - Panangaden, Taylor - 1988 |

3 |
Relative Knowledge and Belief (Extended Abstract
- Fischer, Zuck
- 1987
(Show Context)
Citation Context ...higher level of abstraction using the axioms and inference rules for probabilistic knowledge given by Fagin and Halpern [FH94]. Some progress in this direction has already been made. Fischer and Zuck =-=[FZ87]-=- have used notions of knowledge, probability and complexity theory to analyze a particular interactive proof for quadratic residuosity, and Halpern, Moses, and Tuttle [HMT88] have used related notions... |

2 |
The Cosmic Code: Quantum Mechanics as the Language of Nature. Simon and Schuster
- Pagels
- 1982
(Show Context)
Citation Context ...mber of papers in the philosophical literature (for example, [van80, Lew81]). Interestingly, the same issue arises in quantum mechanics, in Schrodinger's famous cat-in-the-box thought experiment (see =-=[Pag82]-=- for a discussion). We claim that these two choices of probability are best explained in terms of betting games (assuming honest players). At time 0, agent p 1 should certainly be willing to accept an... |

1 |
Fraassen. A temporal framework for conditionals and chance
- van
- 1980
(Show Context)
Citation Context ... so the probability of the coin landing heads is either 0 or 1 (although agent p 1 does not know which). This point of view appears in a number of papers in the philosophical literature (for example, =-=[van80, Lew81]-=-). Interestingly, the same issue arises in quantum mechanics, in Schrodinger's famous cat-in-the-box thought experiment (see [Pag82] for a discussion). We claim that these two choices of probability a... |

1 |
Aknowledge-based analysis of zero knowledge
- Halpern, Moses, et al.
- 1988
(Show Context)
Citation Context ...ay be reasonable, they do not tell us how to makethischoice. One particular (and quite natural) choice is made in [FZ88a] and some arguments are presented for its appropriateness�2 another is made in =-=[HMT88]-=- and used to analyze interactive proof systems. It is not initially clear, however, which choice is most appropriate. In this paper, we clarify the issues involved in choosing the right assignment of ... |