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<p>We propose new intermediate semantics for T-time Petri nets (T-TPN), which fill the gap between strong and weak semantics. By encoding a 2-counter machine, we prove that reachability is not decidable for these semantics in the case of unbounded nets. As regards with bounded nets, we construct a state space abstraction using zones and we study its termination. We then consider safe nets and we propose a translation into interval weighted automata (IWA) over an interval like semiring, product of (max,+) semiring with itself, that preserves the timed behaviour of T-TPN.</p>

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Weakly strong semantics of Time Petri Nets and its algebraic description

  • 期刊论文

  • 发表日期：

    2026年3月25日

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  • Jan Komenda,
  • Sébastien Lahaye,
  • Rémi Parrot,
  • Olivier H. Roux

摘要

We propose new intermediate semantics for T-time Petri nets (T-TPN), which fill the gap between strong and weak semantics. By encoding a 2-counter machine, we prove that reachability is not decidable for these semantics in the case of unbounded nets. As regards with bounded nets, we construct a state space abstraction using zones and we study its termination. We then consider safe nets and we propose a translation into interval weighted automata (IWA) over an interval like semiring, product of (max,+) semiring with itself, that preserves the timed behaviour of T-TPN.