New representations for (max,+) automata with applications to the performance evaluation of discrete event systems

A large class of timed discrete event systems can be modeled thanks to (max,+) automata, that is automata with weights in the so-called (max,+) algebra.In this contribution, new representations are proposed for (max,+) automata. Indeed, specific recursive equations over (max,+) and (min,+) algebras are shown to be suitable for describing extremal behaviors of (max,+) automata. It is underlined that several performance evaluation elements, such as maximum and minimum string execution times, can be easily derived or approximated from these representations.