Modeling of safe time Petri nets by interval weighted automata

Abstract

Abstract Weighted automata with weights (multiplicities) in the product semirings can be viewed as alternative models for timed systems, where concurrent time behaviors are modeled using nondeterminism, while in timed automata using multiple clocks. It is known that safe timed Petri nets can be modeled by means of (max,+) automata, i.e. weighted automata in the (max,+) semiring. We present here a direct way of deriving interval weighted automata with weights in two different product semirings from both safe P-time and safe T-time Petri nets. It is well known that these two classes of time Petri nets are not comparable as opposed to timed Petri nets with deterministic timing of transitions. In terms of weighted automata we need to consider different underlying semirings, namely the product of (max,+) and (min,+) semirings for P-time Petri nets and the product of (max,+) semiring with itself for T-time Petri nets.