Model checking timed automata becomes increasingly complex with the increase in the number of clocks. Hence it is desirable that one constructs an automaton with the minimum number of clocks possible. The problem of checking whether there exists a timed automaton with a smaller number of clocks such that the timed language accepted by the original automaton is preserved is known to be undecidab...

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...

Finite tree automata consist of a set of states and a set of transitions. Input trees are accepted if it is possible to label the tree with states such that the relationship between the state at every node and the state at its child nodes conforms to a transition. Thus, the transitions only define how a state must be labeled with respect to its children or vice versa. This work investigates how...

To each one-dimensional subshift $X$, we may associate a winning shift $W(X)$ which arises from combinatorial game played on the language of $X$. Previously it has been studied what properties $X$ does inherit. For example, and have same factor complexity if is sofic subshift, then also sofic. In this paper, develop notion automaticity for $W(X)$, that is, propose means vector representation ac...