We consider systems consisting of finite automata communicating by exchanging messages and working on the same read-only data. We investigate the situation in which the automata work with constant but different speeds. We assume furthermore that the automata are not aware of the speeds and they cannot measure them directly. Nevertheless, the automata have to compute a correct output. We call this model multi-speed systems of finite automata. Complexity measure that we consider here is the number...

We consider systems consisting of finite automata communicating by exchanging messages and working on the same read-only data. We investigate the situation in which the automata work with constant but different speeds. We assume furthermore that the automata are not aware of the speeds and they cannot measure them directly. Nevertheless, the automata have to compute a correct output. We call this model multi-speed systems of finite automata. Complexity measure that we consider here is the...

J. Hromkovic et al. have given an elegant method to convert a regular expression of size $n$ into an $\epsilon$-free nondeterministic finite automaton having $O\left(n\right)$ states and $O\left(n{log}^2\left(n\right)\right)$ transitions. This method has been implemented efficiently in $O\left(n{log}^2\left(n\right)\right)$ time by C. Hagenah and A. Muscholl. In this paper we extend this method to weighted regular expressions and we show that it can be achieved in $O\left(n{log}^2\left(n\right)\right)$ time.

J. Hromkovic et al. have given an elegant method to convert a regular expression of size n into an ε-free nondeterministic finite automaton having O(n) states and O(nlog2(n)) transitions. This method has been implemented efficiently in O(nlog2(n)) time by C. Hagenah and A. Muscholl. In this paper we extend this method to weighted regular expressions and we show that it can be achieved in O(nlog2(n)) time.