Automaton semigroups

In this thesis, the automaton semigroups and the automaton groups are defined and it is shown that every finite semigroup is an automaton semigroup. If S is an automaton semigroup and S^0 (S^1) is the semigroup formed by adjoining a zero (identity) to S, then it is shown that S^0 (S^1) is also an automaton semigroup and every automaton semigroup is residually finite. Also, it is shown that for any n ≥ 2 with n∈ℕ*, the free commutative semigroup of rank n is an automaton semigroup. In addition, the Cayley automatons and the Cayley automaton semigroups are defined and some relevant theorems are proved. Finally, (3,2)-semigroups, (3,2)-automata and (3,2)-semigroup automata are defined; the method of generating a (3,2)-semigroup automata from (3,2)-automatan is investigated and an algorithm for this method is given.