Compositional semantics for open Petri nets based on deterministic processes

In order to model the behaviour of open concurrent systems by means of Petri nets, we introduce open Petri nets, a generalization of the ordinary model where some places, designated as open, represent an interface of the system towards the environment. Besides generalizing the token game to reflect this extension, we define a truly concurrent semantics for open nets by extending the Goltz-Reisig process semantics of Petri nets. We introduce a composition operation over open nets, characterized as a pushout in the corresponding category, suitable to model both interaction through open places and synchronization of transitions. The process semantics is shown to be compositional with respect to such composition operation. Technically, our result is similar to the amalgamation theorem for data-types in the framework of algebraic specifications. A possible application field of the proposed constructions and results is the modeling of interorganizational workflows, recently studied in the literature. This is illustrated by a running example.

Constructed wetlands are an efficient and cost-effective method of restoring degraded wetlands, in which the microorganisms present make a significant contribution to the ecosystem. In this study, we comprehensively investigated the patterns of diversity and assembly processes of 7 types of constructed wetlands at the rhizosphere and phyllosphere levels. The results showed that the rhizosphere communities of the constructed wetlands exhibited a more balanced structure than that of paddy fields, and 5 types of constructed wetland demonstrated higher potential diversity than that of paddy fields. However, the opposite trend was observed for the phyllosphere communities. Analysis of mean nearest taxon difference indicated that both deterministic and stochastic processes affected the establishment of the rhizosphere and phyllosphere communities, and stochastic processes may have had a larger effect. An iCAMP model showed that dispersal limitation was the most important factor (67% relative contribution) in the rhizosphere community, while drift was the most important (47% relative contribution) in the phyllosphere community. Mantel tests suggested that sucrase, average height, top height, total biomass, belowground biomass, maximum water-holding capacity, and capillary porosity were significantly correlated with processes in the rhizosphere community, whereas factors such as the deterministic process, average height, top height, and SOC were significantly correlated with deterministic processes in the phyllosphere community. Our results can assist in the evaluation of artificial restorations, and can provide understanding of the ecological processes of microbial communities, as well as new insights into the manipulation of microorganisms in polluted wetland ecosystems.

Process versus unfolding semantics for Place/Transition Petri nets

We introduce infinitary partial languages for Petri nets and study some of their properties. Earlier results on the interrelation between various Petri net semantics for finite behaviour are shown to be valid for infinite behaviour. As a consequence step sequences and event structures of processes both can be taken as a semantics for Petri nets without any loss of information.Via the introduction of infinite partial words it is possible to express the properties of justice and fairness in a natural way: justice can be characterized as maximality of progress and fairness as ‘fair’ conflict resolution. By this we overcome the ambiguity arising from the lack of discrimination between concurrency and non-determinism in the sequential approach.

Model checking Petri nets with MSVL

The floodplain ecosystem plays an important role in the mediation or regulation of regional ecological functions, and is the heart of ecosystem functions based on soil microbial communities. In the present study, we investigate the patterns and assembly processes of soil microbial communities along nine profile depths (up to 280 cm in depth) of three stages of floodplain community succession (channel bar, newly deposited river beach and tender floodplain) and farmland in the floodplain of the lower Yellow River. Generally, the bacterial community in agricultural soil had the highest diversity, whereas the archaeal community in the tender floodplain had the highest diversity. Compared to bacteria, the co‐occurrence network of archaea was more complex and stable and had high connectivity. Our data suggest that the resistance of bacteria and archaea to environmental changes in deep soil was higher when compared to that in surface soil. Furthermore, stochastic and deterministic processes acted concurrently to regulate the assembly of the soil microbial community in the floodplain ecosystems. However, the relative contributions of the stochastic process and deterministic process are different between the bacterial community and the archaeal community. The lowest contribution of the stochastic process in the bacterial community was in the subsoil, whereas in the archaeal community, it was the opposite. For ecological selection, bacterial communities in different soil profiles, in the succession stages and in the farmland, were mainly selected through homogeneous selection, whereas archaeal communities were selected through heterogeneous selection. Compared with the three floodplain succession stages, the microbial communities of agricultural lands were more assembled by deterministic processes.Highlights Stochastic and deterministic processes act concurrently to regulate the assembly of soil microbial community in the floodplain ecosystems. The assembly of the bacterial community was mainly affected by the homogeneous selection. The archaeal community was mainly affected by the heterogeneous selection. The microbial communities of agricultural lands were more assembled by deterministic processes.

Understanding biological pathways is an important activity in the biological domain for drug development. Due to the parallelism and complexity inherent in pathways, computer models that can answer queries about pathways are needed. A researcher may ask `what-if' questions comparing alternate scenarios, that require deeper understanding of the underlying model. In this paper, we present overview of such a system we developed and an English-like high level language to express pathways and queries. Our language is inspired by high level action and query languages and it uses Petri Net execution semantics.

Harmful cyanobacterial blooms pose a risk to human health worldwide. To enhance understanding on the bloom-forming mechanism, the spatiotemporal changes in cyanobacterial diversity and composition in two eutrophic lakes (Erhai Lake and Lushui Reservoir) of China were investigated from 2010 to 2011 by high-throughput sequencing of environmental DNA. For each sample, 118 to 260 cpcBA-IGS operational taxonomic units (OTUs) were obtained. Fifty-two abundant OTUs were identified, which made up 95.2% of the total sequences and were clustered into nine cyanobacterial groups. Although the cyanobacterial communities of both lakes were mainly dominated by Microcystis, Erhai Lake had a higher cyanobacterial diversity. The abundance of mixed Nostocales species was lower than that of Microcystis, whereas Phormidium and Synechococcus were opportunistically dominant. The correlation between the occurrence frequency and relative abundance of OTUs was poorly fitted by the Sloan neutral model. Deterministic processes such as phosphorus availability were shown to have significant effects on the cyanobacterial community structure in Erhai Lake. In summary, the Microcystis-dominated cyanobacterial community was mainly affected by the deterministic process. Opportunistically dominant species have the potential to replace Microcystis and form blooms in eutrophic lakes, indicating the necessity to monitor these species for drinking water safety.

Due to the environmental conditions presented in arid zones, it is expected to have a high influence of deterministic processes over the community assemblages. Symbiotic interactions with microorganisms could increase colonization and survival of plants in difficult conditions, independent of the plants physiological and morphological characteristics. In this context, the microbial communities associated to plants that inhabit these types of areas can be a good model to understand the community assembly processes. We investigated the influence of stochastic and deterministic processes in the assemblage of rhizosphere microbial communities of Agave lechuguilla and bulk soil on the Cuatro Cienegas Basin, a site known for its oligotrophic conditions. We hypothesize that rhizospheric microbial communities of A. lechuguilla differ from those of bulk soil as they differ in physicochemical properties of soil and biotic interactions, including not only the plant, but also their microbial co-occurrence networks, it is expected that microbial species usually critical for plant growth and health are more common in the rhizosphere, whereas in the bulk soil microbial species related to the resistance to abiotic stress are more abundant. In order to confirm this hypothesis, 16S rRNA gene was sequenced by Illumina from rhizospheric and bulk soil samples in two seasons, also the physicochemical properties of the soil were determined. Our results showed differences in bacterial diversity, community composition, potential functions, and interaction networks between the rhizosphere samples and the ones from bulk soil. Although community structure arises from a complex interplay between deterministic and stochastic forces, our results suggest that A. lechuguilla recruits specific rhizospheric microbes with functional traits that benefits the plant through growth promotion and nutrition. This selection follows principally a deterministic process that shapes the rhizospheric microbial communities, directed by the plant modifications around the roots but also subjected to the influence of other environmental variables, such as seasonality and soil properties. Interestingly, keystone taxa in the interactions networks, not necessarily belong to the most abundant taxonomic groups, but they have an important role by their functional traits and keeping the connections on the community network.

We propose rewriting logic as a unifying framework for a wide range of nets models. We treat in detail place/transition nets and important extensions of the basic model by individual tokens, test arcs, and time. Based on the idea that Petri nets are monoids suggested by Meseguer and Montanari we define a rewriting semantics that maps place/transition nets into rewriting logic specifications. We furthermore generalize this result to a general form of algebraic net specifications subsuming also colored nets as a special case. The soundness and completeness results we state relate the commutative process semantics of nets proposed by Best and Devillers to the model-theoretic semantics of rewriting logic in the sense of natural isomorphisms between suitable functors. In addition we show how place/transition nets with test arcs and timed nets can be equipped with a rewriting semantics and discuss how other extensions can be treated along similar lines. Beyond the conceptual unification of quite different kinds of nets within a single framework, the rewriting semantics can provide a guide for future extensions of nets and help to cope with the growing diversity of models in this field. On the practical side, a major application of the rewriting semantics is its use as a logical and operational representation of net models for formal verification and for the efficient execution and analysis using a rewriting engine such as Maude, which also allows us to specify different execution and analysis strategies in the same rewriting logic language by means of reflection.

Efficient State Space Search for Time Petri Nets

In the paper, a "truly concurrent" and nondeterministic semantics is defined in terms of branching processes of discrete-time Petri nets (DTPNs). These nets may involve infinite numbers of transitions and places, infinite number of tokens in places, and (maximal) steps of concurrent transitions, which allows us to consider this class of DTPNs to be the most powerful class of Petri nets. It is proved that the unfolding (maximal branching process) of the DTPN is the greatest element of a complete lattice constructed on branching processes of DTPNs with step semantics. Moreover, it is shown that this result is true also in the case of maximal transition steps if additional restrictions are imposed on the structure and behavior of the DTPN.

<p>In many systems a number of different processes have a similar structure and behaviour. To shorten system description and system analysis it is desirable to be able to treat such similar processes in a uniform and succinct way. In this paper it is shown how Petri nets can be generalized to allow processes to be described by a common subnet, without losing the ability to distinguish between them. Our generalization, called coloured Petri nets, is heavily influenced by predicate/transition-nets introduced by H.J. Genrich and K. Lautenbach. Moreover our paper shows how the invariant-method, introduced for Petri nets by K. Lautenbach can be generalized to coloured Petri nets.</p><p>Revised version (first version 1979)</p>

In the area of specification and modelling of concurrent systems, Petri nets have become a standard tool, and they still work behind the scenes in tools for graph transformation systems (cf. [1]). Moreover there is still potential for crossfertilization between the graph transformation and Petri net community. Even a better understanding of adhesive categories [2] and the related concepts of [3] seems possible in light of the proposed notion of weakly adhesive categories [4], which has emerged during work on the generalization of the co-reflective semantics of Petri nets to the realm of graph transformation and adhesive rewriting systems.KeywordsType ObjectGraph TransformationConcurrent SystemGraph GrammarGraph Transformation SystemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

A general stochastic hybrid process (GSHP) is a mathematical formalism that covers most of the requirements posed by the modelling of complex operations, such as time dependencies, multi-dimensional continuous as well as discrete processes, discontinuities, randomness and model uncertainties. In addition, it is possible to study GSHP by using stochastic analysis methodologies, thereby empowering it with powerful mathematical properties. This guarantees unambiguous simulation possibility of the model and allows speeding up this simulation while keeping the model properties intact. However, using GSHP to construct a model of a complex operation is not easy. To support the modelling and the subsequent verification both by mathematical and by multiple operational domain experts, a supporting graphical modelling formalism is desired. Petri nets have shown to be useful for developing models of various complex applications. Typical Petri net features are concurrency and synchronisation mechanism, hierarchical and modular construction, and natural expression of causal dependencies, in combination with graphical and analytical representations. The aim of this thesis is to combine the strengths of Petri net modelling formalisms and those of GSHP. First, dynamically coloured Petri nets (DCPN) are developed, and proof of equivalence is provided with piecewise deterministic Markov processes, which is a particular class of GSHP. Next, DCPN are extended to stochastically and dynamically coloured Petri nets (SDCPN), and proof of equivalence is provided with GSHP. Subsequently, SDCPN are extended to SDCPN with interconnection mapping types (SDCPNimt) and proof of equivalence is provided with both SDCPN and GSHP. It is shown with illustrative air transport examples that these three classes of Petri net are very effective when it comes to the compositional modelling of operations consisting of many distributed components that behave and interact in a dynamic way with many uncertainties. With the equivalence relations between these formalisms, the properties and strengths of the various approaches are combined. The many applications of the approach developed in this thesis, executed at NLR and beyond, show that both the approach and its combined strengths are acknowledged and supported by practice.