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The Resource The mathematics of coordinated inference : a study of generalized hat problems, Christopher S. Hardin, Alan D. Taylor

The mathematics of coordinated inference : a study of generalized hat problems, Christopher S. Hardin, Alan D. Taylor

Creator
Author
Contributor
Summary
Two prisoners are told that they will be brought to a room and seated so that each can see the other. Hats will be placed on their heads;each hat is either red or green. The two prisoners must simultaneouslysubmit a guess of their own hat color, and they both go free if atleast one of them guesses correctly. While no communication is allowedonce the hats have been placed, they will, however, be allowed to havea strategy session before being brought to the room. Is there astrategy ensuring their release? The answer turns out to be yes, and this is the simplest non-trivial example of a hat problem. This book deals with the question of how successfully one can predict the value of an arbitrary function at one or more points of its domainbased on some knowledge of its values at other points. Topics rangefrom hat problems that are accessible to everyone willing to thinkhard, to some advanced topics in set theory and infinitarycombinatorics. For example, there is a method of predicting the valuef(a) of a function f mapping the reals to the reals, based only onknowledge of f's values on the open interval (a 1, a), and for everysuch function the prediction is incorrect only on a countable set that is nowhere dense. The monograph progresses from topics requiring fewer prerequisites to those requiring more, with most of the text being accessible to any graduate student in mathematics. The broad range of readership includes researchers, postdocs, and graduate students in the fields of set theory, mathematical logic, and combinatorics, The hope is that this book will bring together mathematicians from different areas to think about set theory via a very broad array of coordinated inference problems
Language
eng
Work
Publication
Extent
1 online resource.
Contents
  • 1. Introduction
  • 2. The Finite Setting
  • 3. The Denumerable Setting: Full Visibility
  • 4. The Denumerable Setting: One-Way Visibility
  • 5. Dual Hat Problems and the Uncountable
  • 6. Galvin's Setting: Neutral and Anonymous Predictors
  • 7. The Topological Setting
  • 8. Universality of the -Predictor
  • 9. Generalizations and Galois-Tukey Connections
  • Bibliography
  • Index
Isbn
9783319013336
Instance
Label
The mathematics of coordinated inference : a study of generalized hat problems
Title
The mathematics of coordinated inference
Title remainder
a study of generalized hat problems
Statement of responsibility
Christopher S. Hardin, Alan D. Taylor
Creator
Contributor
Author
Subject
Language
eng
Summary
Two prisoners are told that they will be brought to a room and seated so that each can see the other. Hats will be placed on their heads;each hat is either red or green. The two prisoners must simultaneouslysubmit a guess of their own hat color, and they both go free if atleast one of them guesses correctly. While no communication is allowedonce the hats have been placed, they will, however, be allowed to havea strategy session before being brought to the room. Is there astrategy ensuring their release? The answer turns out to be yes, and this is the simplest non-trivial example of a hat problem. This book deals with the question of how successfully one can predict the value of an arbitrary function at one or more points of its domainbased on some knowledge of its values at other points. Topics rangefrom hat problems that are accessible to everyone willing to thinkhard, to some advanced topics in set theory and infinitarycombinatorics. For example, there is a method of predicting the valuef(a) of a function f mapping the reals to the reals, based only onknowledge of f's values on the open interval (a 1, a), and for everysuch function the prediction is incorrect only on a countable set that is nowhere dense. The monograph progresses from topics requiring fewer prerequisites to those requiring more, with most of the text being accessible to any graduate student in mathematics. The broad range of readership includes researchers, postdocs, and graduate students in the fields of set theory, mathematical logic, and combinatorics, The hope is that this book will bring together mathematicians from different areas to think about set theory via a very broad array of coordinated inference problems
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorName
Hardin, Christopher S
Dewey number
511.3
Index
index present
LC call number
QA9
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorDate
1947-
http://library.link/vocab/relatedWorkOrContributorName
Taylor, Alan D.
Series statement
Developments in mathematics
Series volume
volume 33
http://library.link/vocab/subjectName
  • Logic, Symbolic and mathematical
  • MATHEMATICS
  • Logic, Symbolic and mathematical
  • Mathematics
  • Mathematical Logic and Foundations
  • Topology
  • Game Theory, Economics, Social and Behav. Sciences
Label
The mathematics of coordinated inference : a study of generalized hat problems, Christopher S. Hardin, Alan D. Taylor
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
1. Introduction -- 2. The Finite Setting -- 3. The Denumerable Setting: Full Visibility -- 4. The Denumerable Setting: One-Way Visibility -- 5. Dual Hat Problems and the Uncountable -- 6. Galvin's Setting: Neutral and Anonymous Predictors -- 7. The Topological Setting -- 8. Universality of the -Predictor -- 9. Generalizations and Galois-Tukey Connections -- Bibliography -- Index
Control code
861967791
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9783319013336
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-01333-6
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)861967791
Label
The mathematics of coordinated inference : a study of generalized hat problems, Christopher S. Hardin, Alan D. Taylor
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
1. Introduction -- 2. The Finite Setting -- 3. The Denumerable Setting: Full Visibility -- 4. The Denumerable Setting: One-Way Visibility -- 5. Dual Hat Problems and the Uncountable -- 6. Galvin's Setting: Neutral and Anonymous Predictors -- 7. The Topological Setting -- 8. Universality of the -Predictor -- 9. Generalizations and Galois-Tukey Connections -- Bibliography -- Index
Control code
861967791
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9783319013336
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-01333-6
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)861967791

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