Step net bisimilarity \cite{Gor23} is a truly concurrent behavioral equivalence for finite Petri nets, which is defined as a smooth generalization of standard step bisimilarity \cite{NT84} on Petri nets, but with the property of relating markings (of the same size only) generating the same partial orders of events. The process algebra FNM \cite{Gor17} truly represents all (and only) the finite Petri nets, up to isomorphism. We prove that step net 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.
We introduce three general compositionality criteria over operational semantics and prove that, when all three are satisfied together, they guarantee weak bisimulation being a congruence. Our work is founded upon Turi and Plotkin's mathematical operational semantics and the coalgebraic approach to weak bisimulation by Brengos. We demonstrate each criterion with various examples of success and failure and establish a formal connection with the simply WB cool rule format of Bloom and van Glabbeek. In addition, we show that the three criteria induce lax models in the sense of Bonchi et al.
Two formal stochastic models are said to be bisimilar if their solutions as a stochastic process are probabilistically equivalent. Bisimilarity between two stochastic model formalisms means that the strengths of one stochastic model formalism can be used by the other stochastic model formalism. The aim of this paper is to explain bisimilarity relations between stochastic hybrid automata, stochastic differential equations on hybrid space and stochastic hybrid Petri nets. These bisimilarity relations make it possible to combine the formal verification power of automata with the analysis power of…
We propose a framework for the specification of behaviour-preserving reconfigurations of systems modelled as Petri nets. The framework is based on open nets, a mild generalisation of ordinary Place/Transition nets suited to model open systems which might interact with the surrounding environment and endowed with a colimit-based composition operation. We show that natural notions of bisimilarity over open nets are congruences with respect to the composition operation. The considered behavioural equivalences differ for the choice of the observations, which can be single firings or parallel steps…
In 1987 Ernst-Rüdiger Olderog provided an operational Petri net semantics for a subset of CCSP, the union of Milner's CCS and Hoare's CSP. It assigns to each process term in the subset a labelled, safe place/transition net. To demonstrate the correctness of the approach, Olderog established agreement (1) with the standard interleaving semantics of CCSP up to strong bisimulation equivalence, and (2) with standard denotational interpretations of CCSP operators in terms of Petri nets up to a suitable semantic equivalence that fully respects the causal structure of nets. For the latter he employed…
Step net bisimulation is a coinductive behavioral relation for finite Petri nets, which is a smooth generalization of the definition of standard step bisimulation \cite{NT84} on finite Petri nets. Its induced equivalence offers an alternative, much simpler characterization of causal-net bisimilarity \cite{G15,Gor22}, as it does not resort to any causality structure, and of structure-preserving bisimilarity \cite{G15}, as it does not require bijective mappings between related markings. We show that step net bisimilarity can be characterized logically by means of a suitable modal logic, called N…
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.
The operational semantics of interactive systems is usually described by labeled transition systems. Abstract semantics (that is defined in terms of bisimilarity) is characterized by the final morphism in some category of coalgebras. Since the behaviour of interactive systems is for many reasons infinite, symbolic semantics were introduced as a mean to define smaller, possibly finite, transition systems, by employing symbolic actions and avoiding some sources of infiniteness. Unfortunately, symbolic bisimilarity has a different shape with respect to ordinary bisimilarity, and thus the standard…
We formalise a general concept of distributed systems as sequential components interacting asynchronously. We define a corresponding class of Petri nets, called LSGA nets, and precisely characterise those system specifications which can be implemented as LSGA nets up to branching ST-bisimilarity with explicit divergence.
We introduce a novel technique for checking reachability in Petri nets that relies on a recently introduced compositional algebra of nets. We prove that the technique is correct, and discuss our implementation. We report promising experimental results on some well-known examples.
Compositionality and process equivalence are both standard concepts of process algebra. Compositionality means that the behaviour of a compound system relies only on the behaviour of its components, i.e. there is no emergent behaviour. Process equivalence means that the explicit statespace of a system takes a back seat to its interaction patterns: the information that an environment can obtain though interaction. Petri nets are a classical, yet widely used and understood, model of concurrency. Nevertheless, they have often been described as a non-compositional model, and tools tend to deal wit…
This paper presents a modular approach to discover process models for multi-agent systems from event logs. System event logs are filtered according to individual agent behavior. We discover workflow nets for each agent using existing process discovery algorithms. We consider asynchronous interactions among agents. Given a specification of an interaction protocol, we propose a general scheme of workflow net composition. By using morphisms, we prove that this composition preserves soundness of components. A quality evaluation shows the increase in the precision of models discovered by the propos…
This paper presents a compositional conformance checking approach between nested Petri nets and event logs of multi-agent systems. By projecting an event log onto model components, one can perform conformance checking between each projected log and the corresponding component. We formally demonstrate the validity of our approach proving that, to check fitness of a nested Petri net is equivalent to check fitness of each of its components. Leveraging the multi-agent system structure of nested Petri nets, this approach may provide specific conformance diagnostics for each system component as well…
