Place bisimilarity $\sim_p$ is a behavioral equivalence for finite Petri nets, originally proposed in \cite{ABS91}, that, differently from all the other behavioral relations proposed so far, is not defined over the markings of a finite net, rather over its places, which are finitely many. Place bisimilarity $\sim_p$ was claimed decidable in \cite{ABS91}, but its decidability was not really proved. We show that it is possible to decide $\sim_p$ with a simple algorithm, which essentially scans all the place relations (which are finitely many) to check whether they are place bisimulations. We also show that $\sim_p$ does respect the intended causal semantics of Petri nets, as it is finer than causal-net bisimilarity \cite{Gor22}. Moreover, we propose a slightly coarser variant, we call d-place bisimilarity $\sim_d$, that we conjecture to be the coarsest equivalence, fully respecting causality and branching time (as it is finer than fully-concurrent bisimilarity \cite{BDKP91}), to be decidable on finite Petri nets. Finally, two even coarser variants are discussed, namely i-place and i-d-place bisimilarities, which are still decidable, do preserve the concurrent behavior of Petri nets, but do not respect causality. These results open the way towards formal verification (by equivalence checking) of distributed systems modeled by finite Petri nets.
翻译:双相似点 $sim_p$ 是固定的 Petrinet 的一种行为等值, 最初在\ cite{ ABS91} 中提出, 与迄今提出的所有其他行为关系不同, 与目前提议的所有其它行为关系不同, 其定义不是固定网的标记, 而是其位置上的标记, 范围有限。 在\ cite{ ABS91} 中, 双相似点 $\sim_ p$ 被指称为可降为降级 。 此外, 我们提出一个略微粗略的变数, 我们称之为 d-place biciality $\ sim_ d$, 基本上扫描所有地方关系( 范围有限很多) 以检查它们是否是降级的模拟。 我们还表明, $\ sim_ p$ 尊重 Petrinet 的预期因果关系。 因为它比因果关系 相近点 { cite > 。 此外, 我们提出一个略微的变数的变数变量, 我们称 d-place bial reality $_ dealtitudeal respilate) rational reliver raltiquelational raltiquest raltitude) ral ral ral ral relevational ral rviews</s>