Abstract
In this paper we will show that safe timed Petri nets (TPNs) with preselection semantics can be represented by deterministic two-level (max,+) automata (2l-MPA). In 2l-MPA, the outer dynamics, corresponding to the evolution of component clocks, is represented by deterministic Mealy automata with vector-valued outputs from (max,+) semiring. The outer dynamics is then adjusted by inner dynamics corresponding to synchronizations, which are implemented through scalar-like multiplication of the coefficients by symmetric Boolean matrices. These Boolean matrices encode synchronization among the state machines components. The previous approaches encoded either safe TPNs under preselection policy as nondeterministic (max,+) automata, or TPNs under (more restrictive) race policy as deterministic (max,+) automata.
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