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3-state Automata acting on 2-letter alphabet

The set of states is {1,2,3}. Permutation \sigma permutes letters of alphabet.

1 = (,) \sigma^
2 = (,) \sigma^
3 = (,) \sigma^


Number of Automaton is:

The smallest number of automaton generating isomorphic group:

The smallest number of automaton symmetric to the given one:

The smallest number of automaton minimally symmetric to the given one:


This material is based upon work supported by the National Science Foundation under Grants No. 0308985, 0456185 and 0600975.

Updated:
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