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SUMMARY:Toghrul Karimov (MPI-SWS\, IRIF)
DTSTART:20260630T120000Z
DTEND:20260630T130000Z
DTSTAMP:20260513T203848Z
UID:OWNS/169
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/169/">A
 utomata on S-adic words</a>\nby Toghrul Karimov (MPI-SWS\, IRIF) as part o
 f One World Numeration seminar\n\n\nAbstract\nO. Carton and W. Thomas gave
 \, in 2002\, an algorithm for deciding whether a given automaton $A$ over 
 infinite words accept a given morphic word $u$. Together with V. Berthé a
 nd M. Vahanwala\, we study the same automaton acceptance problem in the mo
 re general setting of $S$-adic words. Among other results\, we show how to
  compute\, given a set $S$ of substitutions and an automaton $A$\, an auto
 maton $B$ that accepts a sequence $s$ over $S$ if and only if $s$ directs 
 a word accepted by $A$. Thus we are able to completely answer questions of
  the form "Which Sturmian words $u$ are accepted by a given automaton $A$?
 " In particular\, we show that whether $A$ accepts $u$ is completely deter
 mined by the first $N$ (that depends only on $A$) partial quotients of the
  slope of $u$. Our main tools are monoids and a new (?) structure theorem 
 for $S$-adic expansions.\n
LOCATION:https://researchseminars.org/talk/OWNS/169/
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