Bruni, Riccardo

English

Florence Research

This is a review submitted to Mathematical Reviews/MathSciNet.Reviewer Name: Bruni, RiccardoMathematical Reviews/MathSciNet Reviewer Number: 138582Address:Dipartimento di Lettere e FilosofiaUniversita` di Firenzevia Bolognese 5250139 FlorenceITALYriccardo.bruni@unifi.itAuthor: Cowen, RobertTitle: Adaptive fault diagnosis using self-referential reasoning.MR Number: MR3754094Primary classification:Secondary classification(s):Review text:Imagine that we have launched a spaceship in the outer space with no hu-man crew, and we have instructed processors to test each other. How can wedetect from distance reliable processors from non-reliable ones? The author ofthe paper under review applies to identity faulty computers Smullyan’s NelsonGoodman Principles that allows one to create “Yes or No” questions to dealwith characters such as those who populates his well-known recreational puz-zles, like Knights, who always tell the truth, Knaves, who always tell the false,and Normal, who sometimes tell the truth and sometimes lie (see R. Smullyan,Logical Labyrinths, A.K. Peters, Wellsley, MA, 2009; MR2474164). The saidprinciple is used here to propose a unified approach to the question about howto divide a given set I of individuals into the set R of those who are reliable,and the set U of the unreliable ones. In particular, the aim is to find a so-lution which may work both if one follows the standard treatment and takesonly those individuals who always tell the truth to be reliable, as well as ifone takes the alternative route proposed by the author of the paper and allowsalso those who always lie to be equally regarded as reliable. The strategy istwo-fold: on the one hand, it is based upon building “Yes or No” questionsQ(X,Y ) to ask to individuals X about individuals Y , which are such that (a)a “Yes” answer implies that either X ∈ U or Y ∈ R and (b) a “No” answerimplies that X ∈ U or Y ∈ U; on the other hand, it uses questions Q′(X,Y )such that (a′) a “Yes” answer implies that X ∈ U or Y ∈ U and (b′) a “No”answer implies that X ∈ U or Y ∈ R. First it is shown that one element of1R can be found by asking Q(X,Y ) at most n − b(n) times, where n = |I| andb(n) is the number of 1s in the binary representation of n. Secondly, it is provedthat one can identify all elements of R by asking Q′(X,Y ) at most n+ t times,where again n = |I| and, if u = |U|, then u ≤ t < n/2. The first result isobtained by adapting to the case here at stake the proof by S. Taschuk (seehttp://math.stackexchange.com/questions/115823). The second result uses aproof strategy sketched by P.M. Blecher (see On a logical problem, DiscreteMath., 43, 1983, pp. 107-110; MR0680309).2

Robert Cowen, Adaptive fault diagnosis using self-referential reasoning

https://flore.unifi.it/bitstream/2158/1137632/1/Cowen_Adaptive_Fault_Diagnosis_Review.pdf

Robert Cowen, Adaptive fault diagnosis using self-referential reasoning

Abstract

Similar works

Full text

Available Versions

Florence Research