Recently, Yamamoto presented a new method for the conversion from regular expressions (REs) to non-deterministic finite automata (NFA) based on the Thompson ε-NFA (AT ). The AT automaton has two quotients considered: the suffix automaton Asuf and the prefix automaton, Apre. Eliminating ε-transitions in AT , the Glushkov automaton (Apos) is obtained. Thus, it is easy to see that Asuf and the par...

Every regular expression can be transformed into a Nondeterministic Finite Automaton (NFA) with or without  transitions. A well known algorithm called subset construction technique is used for conversion of NFA into DFA. In this paper, initially, the construction of the position automaton is given for the same. Also, the algorithm to convert this Position Automaton into DFA using subset constr...

A word is called a reset word for a deterministic finite automaton if it maps all the states of the automaton to a unique state. Deciding about the existence of a reset word of a given maximum length for a given automaton is known to be an NP-complete problem. We prove that it remains NP-complete even if restricted to Eulerian automata with binary alphabets, as it has been conjectured by Martyu...

Positions and derivatives are two essential notions in the conversion methods from regular expressions to equivalent finite automata. Partial derivative based methods have recently been extended to regular expressions with intersection. In this paper, we present a position automaton construction for those expressions. This construction generalizes the notion of position making it compatible wit...

We consider probabilistic automata over finite words. Such an automaton defines the language consisting of the set of words accepted with probability greater than a given threshold. We show the existence of a universally non-regular probabilistic automaton, i.e. an automaton such that the language it defines is non-regular for every threshold. As a corollary, we obtain an alternative and very s...

The problem of transforming a lattice into a non-deterministic finite state automaton is non-trivial. We present a transformation algorithm which tracks, for each node of an automaton under construction, the larcs which it reflects and the lattice nodes at their origins and extremities. An extension of the algorithm permits the inclusion of null, or epsilon, arcs in the output automaton. The al...

The main theorem allows an elegant algorithm to be refined into an efficient one. The elegant algorithm for constructing a finite automaton from a regular expression is based on 'derivatives of' regular expressions; the efficient algorithm is based on 'marking of' regular expressions. Derivatives of regular expressions correspond to state transitions in finite automata. When a finite automaton ...

In this paper we show that a recently published finite automaton stream cipher can be considered as quasigroup based cipher. Some additional properties of the discussed are also given.

We devise an algorithm which, given a bounded automaton A, decides whether the group generated by A is finite. The solution comes from description of infinite sequences having A-orbit using deterministic finite-state acceptor. This acceptor can also be used to decide acts level-transitively.

Recently, Yamamoto presented a new method for the conversion from regular expressions (REs) to non-deterministic finite automata (NFA) based on the Thompson ε-NFA (AT). The AT automaton has two quotients discussed: the suffix automaton Asuf and the prefix automaton, Apre. Eliminating ε-transitions in AT, the Glushkov automaton (Apos) is obtained. Thus, it is easy to see that Asuf and the partia...