Abstract
An autonomous automaton is a finite automaton with output in which the input alphabet has cardinality one when special reduced. We define the transition from automata to semigroups via a representation successful if given two incomparable automata (neither simulate the other), the semigroups representing the automata are distinct. We show that representation by the transition semigroup is not successful. We then consider a representation of automata by semigroups of partial transformations. We show that in general transition from automata to semigroups by this representation is not successful either. In fact, the only successful transition presented is the transiton to this semigroup of partial transformations together with its generating set, and in this case success occurs only with autonomous automata.KeywordsCase SuccessFinite AutomatonSuccessful TransitionPartial TransformationDistrict CouncilThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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