In a preceding paper [6], automata have been introduced for words indexed by linear orderings. These automata are a generalization of automata for finite, infinite, bi-infinite, and even transfinite words studied by Büchi. Kleene’s theorem has been generalized to these words. We show that deterministic automata do not have the same expressive power. Despite this negative result, we prove that r...

Kiister, G., On the Hurwitz product of formal power series and automata, Theoretical Computer Science 83 (1991) 261-273. The Hurwitz (shuffle) product defined on formal power series is generalized to matrices and therefore to automata. The resulting constructions are then used to study commutative power series and abstract families of power series. In particular, the families of power series re...

In a preceding paper (Bruyère and Carton, automata on linear orderings, MFCS’01), automata have been introduced for words indexed by linear orderings. These automata are a generalization of automata for finite, infinite, bi-infinite and even transfinite words studied by Büchi. Kleene’s theorem has been generalized to these words. We prove that rational sets of words on countable scattered linea...

Some applications of linear temporal logic (LTL) require to translate formulae of the logic to deterministic ω-automata. There are currently two translators producing deterministic automata: ltl2dstar working for the whole LTL and Rabinizer applicable to LTL(F,G) which is the LTL fragment using only modalities F and G. We present a new translation to deterministic Rabin automata via alternating...

Deterministic finite automata (DFAs) are constructed for various purposes in computational biology. Little attention, however, has been given to the efficient construction of minimal DFAs. In this article, we define simple nondeterministic finite automata (NFAs) and prove that the standard subset construction transforms NFAs of this type into minimal DFAs. Furthermore, we show how simple NFAs c...

The paper is devoted to a mathematical model of concurrency the special case of which is asynchronous system. Distributed asyn-chronous automata are introduced here. It is proved that the Petri nets and transition systems with independence can be considered like the distributed asynchronous automata. Time distributed asynchronous automata are defined in standard way by the map which assigns tim...