Ferenc Gécseg

On a representation of tree automata

Sequential compositions of tree automata, called selective products, are introduced as a connection of processors computing functions. Decidability results are established for the unary case. These results are related to classical automata theory.

On a 0 -n 1 -products of automata

Abstract The power of α 0 -products, ν 1 -products, and α 0 -ν 1 -products of automata is compared. As one of the main results it is shoen that homomorphic representation power of α 0 -ν 1 -products is the same as that of general products if infinite products are permitted. A detailed analysis of the situation when only finite products are allowable is also provided.

Finite isomorphically complete systems

Abstract In the theory of finite automata it is an important problem to characterize such systems of automata from which any automaton can be built under a given composition and representation. Such systems are called complete with respect to the fixed composition and representation. From practical point of view, it is useful to determine those compositions and representations for which there are finite complete systems. In this paper we show that the existence of finite complete systems implies the unboundedness of the feedback dependency of the composition.

On α0-products and α2-products

Abstract On the basis of the Krohn-Rhodes Decomposition Theorem, a necessary and sufficient condition has recently been formulated with regard to the completeness for the α0-product (cascade composition). Here, the force of this result is demonstrated in giving a simple new proof of a theorem that has been a major contribution in studying αi-products: every (homomorphically) complete class for the Gluskov-type product is already complete for the α2-product.

Classes of Tree Languages and DR Tree Languages Given by Classes of Semigroups

In the first section of the paper we give general conditions under which a class of recognizable tree languages with a given property can be defined by a class of monoids or semigroups defining the class of string languages having the same property. In the second part similar questions are studied for classes of (DR) tree languages recognized by deterministic root-to-frontier tree recognizers.

Comments on complete sets of tree automata

Products of tree automata do not preserve the basic properties of homomorphically and metrically complete systems of finite state automata. To remedy it, we have introduced the concept of the quasi-product of tree automata which is only a slightly more general than the product. In this paper we present the main properties of the quasi-product concerning homomorphic and metric representation of tree automata, and compare the representing powers of special quasi-products.