To my mother Maxine, who gave me a love of learning; to Susan, who is as happy and amazed as I am that The Book is finally completed; to Josh, Tim, and Teddy, who are impressed that their father is an Author; and to my late father George, who would have been proud.

No abstract

We argue that the right way to understand distributed protocols is by considering how messages change the state of knowledge of a system. We present a hierarchy of knowledge states that a system may be in, and discuss how communication can move the system's state of knowledge of a fact up the hierarchy. Of special interest is the notion of common knowledge. Common knowledge is an essential state of knowledge for reaching agreements and coordinating action. We show that in practical distributed systems, common knowledge is not attainable. We introduce various relaxations of common knowledge that are attainable in many cases of interest. We describe in what sense these notions are appropriate, and discuss their relationship to each other. We conclude with a discussion of the role of knowledge in distributed systems.

Abstract-A face recognition system must recognize a face from a novel image despite the variations between images of the same face. A common approach to overcoming image variations because of changes in the illumination conditions is to use image representations that are relatively insensitive to these variations. Examples of such representations are edge maps, image intensity derivatives, and images convolved with 2D Gabor-like filters. Here we present an empirical study that evaluates the sensitivity of these representations to changes in illumination, as well as viewpoint and facial expression. Our findings indicated that none of the representations considered is sufficient by itself to overcome image variations because of a change in the direction of illumination. Similar results were obtained for changes due to viewpoint and expression. Image representations that emphasized the horizontal features were found to be less sensitive to changes in the direction of illumination. However, systems based only on such representations failed to recognize up to 20 percent of the faces in our database. Humans performed considerably better under the same conditions. We discuss possible reasons for this superioriority and alternative methods for overcoming illumination effects in recognition.

By anaizng the stares of novledge Li 'he processors attain 19 an urre as.e SYS Tern of a sImp.e tYpe. we capture some o: :rs;c uxder!ying struc t ire of such svsams. particu ar. we study s hat facts become 'on mu kit 0 uiedgc at var:ous ponts in the execu ion of protoco!s n an un reliable system. This characterizes the sirnu Itaneous ac ions hat can he carHed 0:': in s:ch systems. For et ne. we obtain a ccco!e:e charac erizat 0:1 of the nurnSer of ro-iLds rccuired o reach ." ''uUu,eou.s By:anne ,Lq€rr:ent. giver. the pa: tert in hich fa:ares 0CC U. From ri we derive a new protcico: for th: p rbern t ha is optimal in a(l ru7. rarher than just alavs matching the worst-case lower bound. Er some cases this pro? oco a, ains S rnulta ii togs Rvza nt me Agreenient In as few as 2 rounds. e also present a non-trivial simu [tarieou agreement problem called b ualerfl agreement for which there is a protocol that aiways halts in two rounds. Our analysis applies to simultaneous actions in general, and not just to Byzantine agreement. The lower bound proofs presented here generalize and siniplifv ihe previously known proofs.