Automaták teljes rendszereinek és strukturális tulajdonságainak vizsgálata = Studies on complete systems and structural properties of automata

A vizsgálatok elsősorban a faautomaták teljes rendszereire, a determinisztikus felszálló fanyelvek speciális osztályainak a Boole-féle műveletekre való zártsági tulajdonságaira, valamint bizonyos speciális fanyelv-osztályokat megadó monoidok osztályai meghatározására vonatkoztak. Így - Szükséges és elégséges feltételt adtunk arra vonatkozóan, hogy faautomaták egy halmaza izomorfan teljes legyen jól ismert szorzattípusokra nézve az aszinkron faautomaták osztályára vonatkozóan. - Szükséges és elégséges feltételeket adtunk arra vonatkozóan, hogy a nilpotens determinisztikus felszálló fanyelvek osztálya mikor zárt bizonyos logikai műveletekre nézve. - Általános feltételt adtunk meg, amely mellett egy monoid-osztály egyidejűleg meghatározza az ugyanazon tulajdonságokkal bíró közönséges nyelvek és fanyelvek osztályait. | The research carried out in this project concerns mainly complete classes of tree automata, closedness of special classes of deterministic ascending tree languages under Boolean operations, and classes of finite monoids determining certain classes of tree languages. - Necessary and sufficient conditions has been given under which a set of tree automata is isomorphically complete with respect to special types of products for the class of asynchronous tree automa. - Necessary and sufficient conditions has been given under which the class of nilpotent deterministic ascending tree languages is closed under certain logical operations. - General conditions has been given under which a class of finite monids simultenuosly determines a class of string languages and that of tree languages, both language classes having the same properties

Topic, logical subject and sentence structure in Hungarian

This paper investigates the "discourse-configurationality" hypothesis in Hungarian, based on the current assumption that Hungarian sentence structure is largely determined by information structure. It argues for the necessity of differentiating between the notion of topic, defined on a pragmatic level with respect to possible contexts, and the notion of logical subject, defined on a decontextualized logico-semantic level. On the basis of the distinction between these two levels of sentence analysis, Hungarian should be taken as a logical subject-prominent language rather than a topic-prominent one. As for the so-called contrastive topic in Hungarian, only a subclass of contrastive topic expressions meets the topicality conditions established in this paper on a pragmatic ground, and other types of contrastive topic expressions, namely those that can hardly be differentiated from ordinary topics, display the properties of logical subjects rather than topics

Algorithmic decidability of Engel's property for automaton groups

We consider decidability problems associated with Engel's identity ($[\cdots[[x,y],y],\dots,y]=1$ for a long enough commutator sequence) in groups generated by an automaton. We give a partial algorithm that decides, given $x,y$, whether an Engel identity is satisfied. It succeeds, importantly, in proving that Grigorchuk's $2$-group is not Engel. We consider next the problem of recognizing Engel elements, namely elements $y$ such that the map $x\mapsto[x,y]$ attracts to $\{1\}$. Although this problem seems intractable in general, we prove that it is decidable for Grigorchuk's group: Engel elements are precisely those of order at most $2$. Our computations were implemented using the package FR within the computer algebra system GAP