Finite systems are virtually linear

TitleFinite systems are virtually linear

 

SpeakerV. Anashin  (Moscow University)

 

Date: 16:00-17:00 pm; October 31; 2013

 

PlaceConference Room A304, Department of Mathematical Sciences

 

AbstractEvery transducer over an alphabet of $p$ elements maps words of length $N$ to words of length $N$; therefore to every transducer it corresponds a mapping $f$ of finite words to finite words. Every word $W$ of length $N$ can be considered as a base-$p$ expansion of  suitable natural number $w$. A plot of the transducer is  a set of all points $(w/p^N, f(w)/p^N)$ in the unit square. It turns out that if the transducer is finite, the only smooth curves in the plot are straight lines.Possible applications of this result to cryptography and quantum mechanics will  also be discussed.

 

ContactJiayan Yao