True Concurrency Can Be Easy

Net bisimilarity is a behavioral equivalence for finite Petri nets, which is equivalent to structure-preserving bisimilarity and causal-net bisimilarity, but with a much simpler definition, which is a smooth generalization of the definition of standard bisimilarity on Labeled Transition Systems. We show that it can be characterized logically by means of a suitable modal logic, called NML (acronym of net modal logic): two markings are net bisimilar if and only if they satisfy the same NML formulae

Compositional Semantics of Finite Petri Nets

Structure-preserving bisimilarity is a truly concurrent behavioral equivalence for finite Petri nets, which relates markings (of the same size only) generating the same causal nets, hence also the same partial orders of events. The process algebra FNM truly represents all (and only) the finite Petri nets, up to isomorphism. We prove that structure-preserving bisimilarity is a congruence w.r.t. the FMN operators, In this way, we have defined a compositional semantics, fully respecting causality and the branching structure of systems, for the class of all the finite Petri nets. Moreover, we study some algebraic properties of structure-preserving bisimilarity, that are at the base of a sound (but incomplete) axiomatization over FNM process terms.Comment: arXiv admin note: substantial text overlap with arXiv:2301.0448

Decidability of Two Truly Concurrent Equivalences for Finite Bounded Petri Nets

We prove that (strong) fully-concurrent bisimilarity and causal-net bisimilarity are decidable for finite bounded Petri nets. The proofs are based on a generalization of the ordered marking proof technique that Vogler used to demonstrate that (strong) fully-concurrent bisimilarity (or, equivalently, historypreserving bisimilarity) is decidable on finite safe nets

Distributed Non-Interference

Information flow security properties were defined some years ago (see, e.g., the surveys \cite{FG01,Ry01}) in terms of suitable equivalence checking problems. These definitions were provided by using sequential models of computations (e.g., labeled transition systems \cite{GV15}), and interleaving behavioral equivalences (e.g., bisimulation equivalence \cite{Mil89}). More recently, the distributed model of Petri nets has been used to study non-interference in \cite{BG03,BG09,BC15}, but also in these papers an interleaving semantics was used. We argue that in order to capture all the relevant information flows, truly-concurrent behavioral equivalences must be used. In particular, we propose for Petri nets the distributed non-interference property, called DNI, based on {\em branching place bisimilarity} \cite{Gor21b}, which is a sensible, decidable equivalence for finite Petri nets with silent moves. Then we focus our attention on the subclass of Petri nets called {\em finite-state machines}, which can be represented (up to isomorphism) by the simple process algebra CFM \cite{Gor17}. DNI is very easily checkable on CFM processes, as it is compositional, so that it does does not suffer from the state-space explosion problem. Moreover, we show that DNI can be characterized syntactically on CFM by means of a type system

A Decidable Equivalence for a Turing-Complete, Distributed Model of Computation

Place/Transition Petri nets with inhibitor arcs (PTI nets for short), which are a well-known Turing-complete, distributed model of computation, are equipped with a decidable, behavioral equivalence, called pti-place bisimilarity, that conservatively extends place bisimilarity defined over Place/Transition nets (without inhibitor arcs). We prove that pti-place bisimilarity is sensible, as it respects the causal semantics of PTI nets

Place Bisimilarity is Decidable, Indeed!

Place bisimilarity is a behavioral equivalence for finite Petri nets, proposed by Schnoebelen and co-workers in 1991. Differently from all the other behavioral relations proposed so far, a place bisimulation is not defined over the markings of a finite net, rather over its places, which are finitely many. However, place bisimilarity is not coinductive, as the union of place bisimulations may be not a place bisimulation. Place bisimilarity was claimed decidable in [1], even if the algorithm used to this aim [2] does not characterize this equivalence, rather the unique maximal place bisimulation which is also an equivalence relation; hence, its decidability was not proved. Here we show that it is possible to decide place bisimilarity with a simple, yet inefficient, algorithm, which essentially scans all the place relations (which are finitely many) to check whether they are place bisimulations. Moreover, we propose a slightly coarser variant, we call d-place bisimilarity, that we conjecture to be the coarsest equivalence, fully respecting causality and branching time, to be decidable on finite Petri nets

Branching Place Bisimilarity

Place bisimilarity is a behavioral equivalence for finite Petri nets, proposed in \cite{ABS91} and proved decidable in \cite{Gor21}. In this paper we propose an extension to finite Petri nets with silent moves of the place bisimulation idea, yielding {\em branching} place bisimilarity $\approx_p$, following the intuition of branching bisimilarity \cite{vGW96} on labeled transition systems. We also propose a slightly coarser variant, called branching {\em d-place} bisimilarity $\approx_d$, following the intuition of d-place bisimilarity in \cite{Gor21}. We prove that $\approx_p$ and $\approx_d$ are decidable equivalence relations. Moreover, we prove that $\approx_d$ is strictly finer than branching fully-concurrent bisimilarity \cite{Pin93,Gor20c}, essentially because $\approx_d$ does not consider as unobservable those $\tau$-labeled net transitions with pre-set size larger than one, i.e., those resulting from (multi-party) interaction.Comment: arXiv admin note: text overlap with arXiv:2104.01392, arXiv:2104.1485

Decidability of Two Truly Concurrent Equivalences for Finite Bounded Petri Nets

We prove that the well-known (strong) fully-concurrent bisimilarity and the novel i-causal-net bisimilarity, which is a sligtlhy coarser variant of causal-net bisimilarity, are decidable for finite bounded Petri nets. The proofs are based on a generalization of the ordered marking proof technique that Vogler used to demonstrate that (strong) fully-concurrent bisimilarity (or, equivalently, history-preserving bisimilarity) is decidable on finite safe nets