Monotone Rational Series and Max-plus Algebraic Models of Real-time Systems
نویسندگان
چکیده
In the modelling of timed discrete event systems, one traditionally uses dater functions, which give completion times, as a function of numbers of events. Dater functions are non-decreasing. We extend this modelling to the case of multiform logical and physical times, which are needed to model concurrent behaviors. We represent event sequences and time instants by words. A dater is a map, which associates to a word a word, or a set of words, and which is non-decreasing for the subword order. The formal series associated with these generalized dater functions live in a finitely presented semiring, which is equipped with some remarkable relations, due to the monotone character of daters. The implementation of this semiring relies on a theory of rational and recognizable series whose coefficients form a non-decreasing sequence in an idempotent semiring, that we sketch. Finally, we apply this formalism to the modelling and analysis of an elementary example of real time system.
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