605 research outputs found
The finiteness of a group generated by a 2-letter invertible-reversible Mealy automaton is decidable
We prove that a semigroup generated by a reversible two-state Mealy automaton
is either finite or free of rank 2. This fact leads to the decidability of
finiteness for groups generated by two-state or two-letter
invertible-reversible Mealy automata and to the decidability of freeness for
semigroups generated by two-state invertible-reversible Mealy automata
Automata theory in nominal sets
We study languages over infinite alphabets equipped with some structure that
can be tested by recognizing automata. We develop a framework for studying such
alphabets and the ensuing automata theory, where the key role is played by an
automorphism group of the alphabet. In the process, we generalize nominal sets
due to Gabbay and Pitts
Groups generated by 3-state automata over a 2-letter alphabet, I
An approach to a classification of groups generated by 3-state automata over
a 2-letter alphabet and the current progress in this direction are presented.
Several results related to the whole class are formulated. In particular, all
finite, abelian, and free groups are classified. In addition, we provide
detailed information and complete proofs for several groups from the class,
with the intention of showing the main methods and techniques used in the
classification.Comment: 37 pages, 52 figure
From self-similar groups to self-similar sets and spectra
The survey presents developments in the theory of self-similar groups leading
to applications to the study of fractal sets and graphs, and their associated
spectra
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