ON THE FINITENESS PROBLEM FOR AUTOMATON (SEMI)GROUPS
2012 ◽
Vol 22
(06)
◽
pp. 1250052
◽
Keyword(s):
This paper addresses a decision problem highlighted by Grigorchuk, Nekrashevich, and Sushchanskiĭ, namely the finiteness problem for automaton (semi)groups. For semigroups, we give an effective sufficient but not necessary condition for finiteness and, for groups, an effective necessary but not sufficient condition. The efficiency of the new criteria is demonstrated by testing all Mealy automata with small stateset and alphabet. Finally, for groups, we provide a necessary and sufficient condition that does not directly lead to a decision procedure.
2019 ◽
Vol 33
(10)
◽
pp. 1950086
2009 ◽
Vol 86
(1)
◽
pp. 45-60
◽
2016 ◽
Vol 62
(3)
◽
pp. 267-272
2007 ◽
Vol 38
(3)
◽
pp. 267-276
◽
1990 ◽
Vol 33
(4)
◽
pp. 482-488
◽
2015 ◽
Vol 2015
◽
pp. 1-11
◽