Gustav Feichtinger

Bio: Gustav Feichtinger is an academic researcher from IBM. The author has contributed to research in topics: Automorphism & Inner automorphism. The author has an hindex of 1, co-authored 1 publications receiving 11 citations.

Some results on the relation between automata and their automorphism groups

Abstract: In this paper the structure of automata is investigated using the concept of the automorphism group. The investigations about strongly connected automata are extended to cyclic (Oehmke) and normal automata. The set of states is divided into equivalence classes of strongly connected subsets (SCEC). In the set of all SCEC we explain a partial ordering whose minimal elements are called sourceclasses. If there is only one source-classe, the automaton is called cyclic. If each automorphism maps every SCEC onto itself, then the automaton is said to be normal. We generalize some results ofA. Fleck [1]. In some cases we restrict ourselves to Abelian automata.

On the endomorphisms of finite automata

Abstract: The properties of endomorphisms and automorphisms of a finite, deterministic automatonA related to the smallest input-independent partition on the set of internal states ofA are investigated. The setH d of all thed-endomorphisms ofA defined here, as well as the setG d of all thed-automorphisms ofA, are studied in detail. It is proved thatH d forms a polyadic semigroup, whileG d forms a polyadic group. Connections betweenG d and the groupG(A) of all the automorphisms ofA are examined. The upper bound for the cardinality ofG d is given. Finally, by means of the theory ofd-automorphisms, some problems of the theory of strictly periodic automata are solved; in the first place, the necessary and sufficient condition for the reducibility of an arbitrary strictly periodic automation is given.

Periodic Representations and T-Partitionable Equivalents of Sequential Machines

Abstract: This paper deals with the problem of finding nontrivial periodic representations, with not necessarily null transient duration, of deterministic sequential machines. The well-known results in this area, based on means of d-equivalence partitions or regular d-partitions on the set of internal states of a sequential machine A, are generalized. Apart from this, the problem of finding nontrivial periodic representations of A is solved here by the well-known methods of input-independent partitions on the set of internal states of A and by the operation of the (τ, T) numeration introduced here.

Der Quotientenautomat nach einem direkten Faktor einer Automorphismengruppe

Abstract: Jeder UntergruppeH der Automorphismengruppe eines Automaten kann der Quotientenautomat nachH zugeordnet werden, wenn man die Transitivitatsklassen bezuglichH als dessen innere Zustande definiert. Fur starke Automaten, deren Automorphismengruppe ein direktes ProduktH×L als Untergruppe besitzt, wird bewiesen, das die Faktorgruppe der Automorphismenuntergruppe nach einem FaktorH isomorph ist zu einer Automorphismengruppe des Quotientenautomaten moduloH.