Adam Woryna

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In the paper, we deal with the notion of an automaton over a changing alphabet, which generalizes the concept of a Mealy-type automaton. We modify the methods based on the idea of a dual automaton and its action used by B. Steinberg et al. (2011) and M. Vorobets and Ya. Vorobets (2007, 2010) [16–18] and adapt them to automata over a changing alphabet. We(More)
Generalizing the idea of self-similar groups defined by Mealy automata, we introduce the notion of a self-similar automaton and a self-similar group over a changing alphabet. We show that every finitely generated residually-finite group is self-similar over an arbitrary unbounded changing alphabet. We construct some naturally defined self-similar automaton(More)
For every natural number n ≥ 2 and every finite sequence L of natural numbers, we consider the set UDn(L) of all uniquely decodable codes over an n-letter alphabet with the sequence L as the sequence of code word lengths, as well as its subsets PRn(L) and FDn(L) consisting of, respectively, the prefix codes and the codes with finite delay. We derive the(More)
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