Automata, Groups, Limit Spaces, and Tilings

We explore the connections between automata, groups, limit spaces of self-similar actions, and tilings. In particular, we show how a group acting ``nicely'' on a tree gives rise to a self-covering of a topological groupoid, and how the group can be reconstructed from the groupoid and its covering. The connection is via finite-state automata. These define decomposition rules, or self-similar tilings, on leaves of the solenoid associated with the covering.Comment: to appear in J. Algebr

On the Finiteness Problem for Automaton (Semi)groups

This paper addresses a decision problem highlighted by Grigorchuk, Nekrashevich, and Sushchanskii, namely the finiteness problem for automaton (semi)groups. For semigroups, we give an effective sufficient but not necessary condition for finiteness and, for groups, an effective necessary but not sufficient condition. The efficiency of the new criteria is demonstrated by testing all Mealy automata with small stateset and alphabet. Finally, for groups, we provide a necessary and sufficient condition that does not directly lead to a decision procedure

Genetic analysis of line "Lupinoid" of garden pea (Pisum sativum L.)

В исследовании генетического контроля формирования особого типа соцветия линии гороха посевного «Люпиноид» применен гибридологический метод. Показано, что формирование такого соцветия — обусловлено — комплементарным взаимодействием рецессивных аллелей двух генов, один из которых связан с ограничением размеров побеговой апикальной меристемы, а второй контролирует пролиферацию главной оси. Обсуждается возможность использования данной линии в исследовании фундаментальных и прикладных аспектов генетики растений.The hybridological method was used to analyze the genetic control of inflorescence development in pea line "Lupinoid". It was demonstrated that recessive alleles of two genes take part in formation of the special inflorescence type. One of these genes limits size of stem apical meristem, the another one provides axis proliferation in wild type plants. Some conclusions connected with perspectives of usage of analyzed line in plant breeding were also discussed