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SUMMARY:Pavel Semukhin (University of Oxford)
DTSTART:20210608T130000Z
DTEND:20210608T140000Z
DTSTAMP:20260423T022815Z
UID:CTA/58
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CTA/58/">The
  Membership Problem for 2x2 integer matrices</a>\nby Pavel Semukhin (Unive
 rsity of Oxford) as part of Computability theory and applications\n\n\nAbs
 tract\nThe Membership Problem for matrix semigroups is stated as follows: 
 given a finite collection of square matrices F = { M_1\,...\,M_k } and a t
 arget matrix M\, decide if M can be presented as a product of matrices fro
 m F. In other words\, decide if M belongs to the semigroup <F> generated b
 y F. It has been known for a long time that the Membership Problem is unde
 cidable for 3x3 matrices. On the other hand\, it is a big open question wh
 ether this problem is decidable for 2x2 matrices or for some special cases
  of 3x3 matrices.\n\nIn our recent work\, we showed that the Membership Pr
 oblem is decidable for 2x2 nonsingular integer matrices. In this talk\, I 
 will present a proof of this result which is based on a combination of dif
 ferent ideas from linear algebra\, group theory\, and automata theory.\n
LOCATION:https://researchseminars.org/talk/CTA/58/
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