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DTSTART:19700329T010000
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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Finite-State Mutual Dimension - Adam Case (Drake U
niversity)
DTSTART;TZID=Europe/London:20220607T160000
DTEND;TZID=Europe/London:20220607T170000
UID:TALK174806AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/174806
DESCRIPTION:In this talk\, I will discuss recent work with Jac
k H. Lutz on a notion of finite-state mutual dimen
sion. Intuitively\, the finite-state dimension of
a sequence S represents the density of finite-stat
e information contained within S\, while the finit
e-state mutual dimension between two sequences S a
nd T represents the density of finite-state inform
ation shared by S and T. Thus &ldquo\;finite-state
mutual dimension&rdquo\; can be viewed as a &ldqu
o\;finite-state&rdquo\; version of mutual dimensio
n and as a &ldquo\;mutual&rdquo\; version of finit
e-state dimension. The main results that will be d
iscussed are as follows. First\, we show that fini
te-state mutual dimension\, defined using informat
ion-lossless finite-state compressors\, has all of
the properties expected of a measure of mutual in
formation. Next\, we prove that finite-state mutua
l dimension may be characterized in terms of block
mutual information rates. Finally\, we provide ne
cessary and sufficient conditions for two normal s
equences to achieve finite-state mutual dimension
zero.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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