The aim of the paper is to concoct a novel algorithm for the metamorphosis of parallel regular expressions to ε-free nondeterministic finite automata. For a given parallel regular expression r, let m be the number of symbols that occur in r and let C denote the number of concatenation operators in r. In the worst case, 2m+1 states are required for the construction of the non-deterministic finit...

We define a complexity measure on non-deterministic Büchi automata, based on the notion of the width of the skeleton tree introduced by Kähler and Wilke. We show that the induced hierarchy tightly correlates to the Wagner Hierarchy, a corner stone in the theory of regular ω-languages that is derived from a complexity measure on deterministic Muller automata. The relation between the hierarchies...

Previously, self-verifying symmetric difference automata were defined and a tight bound of 2n−1−1 was shown for state complexity in the unary case. We now consider the non-unary case and show that, for every n≥ 2, there is a regular languageLn accepted by a non-unary self-verifying symmetric difference nondeterministic automaton with n states, such that its equivalent minimal deterministic fini...

The subject of this paper are infinite, locally finite, vertex-transitive median graphs. It is shown that the finiteness of the Θ-classes of such graphs does not guarantee finite blocks. Blocks become finite if, in addition, no finite sequence of Θ-contractions produces new cut-vertices. It is proved that there are only finitely many vertex-transitive median graphs of given finite degree with f...

This paper is concerned with the logical control of hybrid control systems (HCS). It is assumed that a discrete-event system PES) plant model has already been extracted from the continuous-time plant. The problem of hybrid control system design can then be solved by applying logical DES controller synthesis techniques to the extracted DES plant. Traditional DES synthesis methods, however, are n...

We introduce and investigate input-driven stack automata, which are a generalization of input-driven pushdown automata that recently became popular under the name visibly pushdown automata. Basically, the idea is that the input letters uniquely determine the operations on the pushdown store. This can nicely be generalized to stack automata by further types of input letters which are responsible...

Determining the minimum number of states required by a finite automaton to separate a given pair of different words is an important problem. In this paper, we consider this problem for quantum automata (QFAs). We show that 2-state QFAs can separate any pair of words in nondeterministic acceptance mode and conjecture that they can separate any pair also with zero-error. Then, we focus on (a more...

In good for games (GFG) automata, it is possible to resolve nondeterminism in a way that only depends on the past and still accepts all the words in the language. The motivation for GFG automata comes from their adequacy for games and synthesis, wherein general nondeterminism is inappropriate. We continue the ongoing effort of studying the power of nondeterminism in GFG automata. Initial indica...

This paper is devoted to the study of nondeterministic closure automata, that is, nondeterministic finite automata (nfas) equipped with a strict closure operator on the set of states and continuous transition structure. We prove that for each regular language L there is a unique minimal nondeterministic closure automaton whose underlying nfa accepts L. Here minimality means no proper sub or quo...

We present Piecewise Deterministic Timed I/O Automata (PDTIOA): a new continuous state automaton model that allows both nondeterministic and probabilistic discrete transitions, along with continuous deterministic trajectories. We use a partition of actions, called tasks and a task scheduler to resolve nondeterministic choice over actions. We define a topology on the set of trajectories and make...