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3-state Automata acting on 2-letter alphabet

This is a scipt accompanying the paper:

For a given 3-state 2-letter automaton it allows to compute the numbers of representatives of symmetry, minimal symmetry, and isomorphism classes. Also it returns some available information about each group. It can also be used in the converse direction: given a number of automaton it will construct the automaton itself. Additional information about each group can be obtained from the paper, and using the AutomGrp package for GAPsystem.

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

1 = (,) σ^
2 = (,) σ^
3 = (,) σ^

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:

Beginning of the growth function:

Ergodicity of automaton:

The log2 of the sizes of G/StG(n):

Small relations:

This material is based upon work supported by the Proposal Enhancement Grant from the USF Internal Awards Program and was prepared in collaboration with Junyi Tu.

Updated: December 06th, 2014
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