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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Finite-State Mutual Dimension

## Finite-State Mutual DimensionAdd to your list(s) Download to your calendar using vCal - Adam Case (Drake University)
- Tuesday 07 June 2022, 16:00-17:00
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact nobody. SASW09 - International conference on computability, complexity and randomness In this talk, I will discuss recent work with Jack H. Lutz on a notion of finite-state mutual dimension. Intuitively, the finite-state dimension of a sequence S represents the density of finite-state information contained within S, while the finite-state mutual dimension between two sequences S and T represents the density of finite-state information shared by S and T. Thus “finite-state mutual dimension” 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 be discussed are as follows. First, we show that finite-state mutual dimension, defined using information-lossless finite-state compressors, has all of the properties expected of a measure of mutual information. Next, we prove that finite-state mutual dimension may be characterized in terms of block mutual information rates. Finally, we provide necessary and sufficient conditions for two normal sequences to achieve finite-state mutual dimension zero. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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