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SUMMARY:Adam Case (Drake University)
DTSTART:20220303T190000Z
DTEND:20220303T200000Z
DTSTAMP:20260423T035629Z
UID:OLS/85
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OLS/85/">Fin
 ite-State Mutual Dimension</a>\nby Adam Case (Drake University) as part of
  Online logic seminar\n\n\nAbstract\nIn this talk\, I will discuss recent 
 work with Jack H. Lutz on a notion of finite-state mutual dimension. Intui
 tively\, the finite-state dimension of a sequence S represents the density
  of finite-state information contained within S\, while the finite-state m
 utual dimension between two sequences S and T represents the density of fi
 nite-state information shared by S and T. Thus "finite-state mutual dimens
 ion" can be viewed as a "finite-state" version of mutual dimension and as 
 a "mutual" version of finite-state dimension. The main results that will b
 e discussed are as follows. First\, we show that finite-state mutual dimen
 sion\, defined using information-lossless finite-state compressors\, has a
 ll of the properties expected of a measure of mutual information. Next\, w
 e prove that finite-state mutual dimension may be characterized in terms o
 f block mutual information rates. Finally\, we provide necessary and suffi
 cient conditions for two normal sequences to achieve finite-state mutual d
 imension zero.\n
LOCATION:https://researchseminars.org/talk/OLS/85/
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