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DTSTART:20250309T070000
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DTSTART:20251102T060000
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UID:69f42ae7e4c09
DTSTART;TZID=America/Toronto:20260223T130000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20260223T143000
URL:https://uwaterloo.ca/pure-mathematics/events/computability-learning-sem
 inar-165
SUMMARY:Computability Learning Seminar
CLASS:PUBLIC
DESCRIPTION:WILLIAM DAN\, UNIVERSITY OF WATERLOO\n\n_A Characterization of 
 Random\, Left C.E. Reals_\n\nAn immediate property of the halting probabil
 ity of a prefix-free\nmachine is that it is a left c.e. real. An easycorol
 lary of the\nKraft-Chaitin theorem is that the converse is true: any left 
 c.e. real\nis the halting probability ofsome prefix-free machine. The most
  common\nexample of a random real is Chaitin's omega\, the haltingprobabil
 ity of\na universal prefix-free machine. In fact\, it is a random left c.e
 .\nreal. It is natural then to ask if theconverse holds in this case as\nw
 ell: that any random left c.e. real is the halting probability of\nsome un
 iversalprefix-free machine. As it turns out\, this is the case\,\nand in t
 his talk I will explain the concept used to solve\nthisquestion\, Solovay 
 reducibility\, then prove the theorems\ndemonstrating the converse. This t
 alk follows sections9.1 and 9.2 of\nthe Downey and Hirschfeldt book. \n\nM
 C 5403
DTSTAMP:20260501T042407Z
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