Extension Of Nets Research Articles

Mobility‐aware modeling and evaluation of IoT systems using stochastic reward nets

SummaryThe frequent geographical changes of mobile nodes in Internet of Things (IoT) systems affect communication, activities, and behaviors. In such scenarios, it is crucial to establish a system model capable of evaluating quality of service (QoS) measures. However, the existing formal modeling techniques pose complexities in modeling mobility. To deal with these challenges, this study aims to propose a model that simplifies the process of modeling mobility within IoT systems. This paper presents a method for modeling mobility within IoT systems by leveraging a widely recognized extension of stochastic Petri nets known as stochastic reward nets (SRNs). The proposed method enhances the SRN model by incorporating the location concept, resulting in a novel extension called mobile SRN (MSRN). In this work, a case study utilizes the MSRN to evaluate the suggested features, examining various scenarios and investigating the impact of factors such as environmental conditions, sensor sampling rate, and the permissible distance of the node from the sink.

Formal Modeling and Verification of Embedded Real-Time Systems: An Approach and Practical Tool Based on Constraint Time Petri Nets

Modeling and verification of the correct behavior of embedded real-time systems with strict timing constraints is a well-known and important problem. Failing to fulfill a deadline in system operation can have severe consequences in the practical case. This paper proposes an approach to formal modeling and schedulability analysis. A novel extension of Petri Nets named Constraint Time Petri Nets (C-TPN) is developed, which enables the modeling of a collection of interdependent real-time tasks whose execution is constrained by the use of priority and shared resources like processors and memory data. A C-TPN model is reduced to a network of Timed Automata in the context of the popular Uppaal toolbox. Both functional and, most importantly, temporal properties can be assessed by exhaustive model checking and/or statistical model checking based on simulations. This paper first describes and motivates the proposed C-TPN modeling language and its formal semantics. Then, a Uppaal translation is shown. Finally, three models of embedded real-time systems are considered, and their properties are thoroughly verified.

Cross-Department Collaborative Healthcare Process Model Discovery From Event Logs

Healthcare plays an increasingly essential role in our daily life. Modern Hospital Information Systems (HISs) record and store detailed medical treatment process information for all patients as event logs. By taking event logs as input, process mining techniques have been widely applied to extract valuable insights to improve medical treatment processes and deliver better healthcare services. However, considering the complexity of collaborations among different medical departments, existing model discovery techniques cannot be applied directly. To handle this limitation, this paper proposes a novel approach to support the discovery of Cross-department Collaborative Healthcare Process (CCHP) models from medical event logs. Specifically, an extension of classical Petri Nets with message and resource attributes is first introduced to formalize CCHPs. Then, a novel discovery algorithm is proposed to discover Intra-department Healthcare Process (IHP) models. Next, collaboration patterns among medical departments are formalized and corresponding discovery algorithms are given on that basis. Finally, a global CCHP model is obtained by integrating all discovered collaboration patterns and IHP models. By using four public medical event logs, we quantitatively compare our approach with the state-of-the-art process mining techniques in terms of model quality, and our experimental results demonstrate that the proposed approach can discover more accurate healthcare process models. <i>Note to Practitioners</i>&#x2014;The recorded medical event logs by HISs can be used to extract valuable insights for the analysis of healthcare processes. However, existing process model discovery techniques cannot be applied for the analysis directly due to the complex collaborations among different medical departments of a hospital. This paper introduces a novel approach for cross-department collaborative healthcare process model discovery from medical event logs. All proposed techniques are fully implemented and publicly available. Using four public medical event logs, we show the applicability and advantages of our approach against existing ones. The proposed techniques are applicable to the model discovery and behavior understanding of real-life operational healthcare processes.

Formal Modeling and Discovery of Multi-instance Business Processes: A Cloud Resource Management Case Study

Process discovery, as one of the most challenging process analysis techniques, aims to uncover business process models from event logs. Many process discovery approaches were invented in the past twenty years; however, most of them have difficulties in handling multi-instance sub-processes. To address this challenge, we first introduce a multi-instance business process model (MBPM) to support the modeling of processes with multiple sub-process instantiations. Formal semantics of MBPMs are precisely defined by using multi-instance Petri nets (MPNs) that are an extension of Petri nets with distinguishable tokens. Then, a novel process discovery technique is developed to support the discovery of MBPMs from event logs with sub-process multi-instantiation information. In addition, we propose to measure the quality of the discovered MBPMs against the input event logs by transforming an MBPM to a classical Petri net such that existing quality metrics, e.g., fitness and precision, can be used. The proposed discovery approach is properly implemented as plugins in the ProM toolkit. Based on a cloud resource management case study, we compare our approach with the state-of-the-art process discovery techniques. The results demonstrate that our approach outperforms existing approaches to discover process models with multi-instance sub-processes.

Characterising bed-parallel slip during gravity-driven deformation

Despite the recognition that bed-parallel slip (BPS) must operate during gravity-driven deformation of basinal sediments, there is a general paucity of detailed outcrop-based observations to characterise and detect such a process. We therefore present detailed timing relationships between BPS and steeper dip-slip faults that were both created during seismically-triggered downslope-directed movement of sediments. Using the late Pleistocene Lisan Formation that was deposited around the Dead Sea Basin as our case study, we show that ‘sub-seismic’ decametric scale BPS planes may pre-date, post-date, or operate coevally with steeper faults generated as sediments slip downslope towards the depocentre. Older BPS can be recognised by sediment injections and minor folds and fractures, whereas younger BPS displaces marker faults downslope towards the basin. BPS operating coevally with steeper faults results in complex overprinting and development of fault-bound lenses. BPS that forms along single surfaces in the footwall of normal faults becomes separated into two distinct planes in the downthrown hangingwall block, indicating broadly coeval development. Adjacent BPS planes that operate synchronously result in synthetic and antithetic faults that ‘hard-link’ and transfer displacement between BPS planes. Attenuated bedding between segments of BPS that overlap and terminate next to one another suggests that ‘soft-linkage’ also forms between coeval BPS planes. Displacement-length relationships of measured BPS planes plot in the same range as recorded for normal faults, although BPS with larger displacements have relatively ‘short’ lengths, suggesting that complete BPS planes are missing due to limitations of outcrop size. Although the lack of displaced bedding across BPS makes it largely invisible on seismic sections across large-scale gravity-driven systems, it does potentially contribute towards the apparent inbalance between net extension and contraction observed in many sections across mass transport deposits. In addition, the realisation that BPS interacts with dip-slip faults to create repeated and missing sections that are particularly focussed along earlier deformed horizons and turbidites, has implications for palaeoseismic studies that assume broadly continuous stratigraphy.

A Generalized Linear Joint Trained Framework for Semi-Supervised Learning of Sparse Features

The elastic net is among the most widely used types of regularization algorithms, commonly associated with the problem of supervised generalized linear model estimation via penalized maximum likelihood. Its attractive properties, originated from a combination of ℓ1 and ℓ2 norms, endow this method with the ability to select variables, taking into account the correlations between them. In the last few years, semi-supervised approaches that use both labeled and unlabeled data have become an important component in statistical research. Despite this interest, few researchers have investigated semi-supervised elastic net extensions. This paper introduces a novel solution for semi-supervised learning of sparse features in the context of generalized linear model estimation: the generalized semi-supervised elastic net (s2net), which extends the supervised elastic net method, with a general mathematical formulation that covers, but is not limited to, both regression and classification problems. In addition, a flexible and fast implementation for s2net is provided. Its advantages are illustrated in different experiments using real and synthetic data sets. They show how s2net improves the performance of other techniques that have been proposed for both supervised and semi-supervised learning.

A Compositional Approach for Complex Event Pattern Modeling and Transformation to Colored Petri Nets with Black Sequencing Transitions

Prioritized Colored Petri Nets (PCPNs) are a well-known extension of plain Petri nets in which transitions can have priorities and the tokens on the places carry data information. In this paper, we propose an extension of the PCPN model with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">black sequencing transitions</i> (BPCPN). This extension allows us to easily model the ordered firing of the same transition using an ordered set of tokens on one of its precondition places. Black sequencing transitions are then presented as a shorthand notation in order to model the processing of a flow of events, represented by one of their precondition places. We then show how black sequencing transitions can be encoded into PCPNs, and their application to model Complex Event Processing (CEP), defining a compositional approach to translate some of the most relevant event pattern operators. We have developed MEdit4CEP-BPCPN, an extension of the MEdit4CEP tool, to provide tool support for this novel technique, thus allowing end users to easily define event patterns and obtain an automatic translation into BPCPNs. This can, in turn, be transformed into a corresponding PCPN, and then be immediately used in CPN Tools. Finally, a health case study concerning the monitoring of pregnant women is considered to illustrate how the event patterns are created and how the BPCPN and PCPN models are obtained by using the MEdit4CEP-BPCPN tool.

Acyclic and Cyclic Reversing Computations in Petri Nets

Reversible computations constitute an unconventional form of computing where any sequence of performed operations can be undone by executing in reverse order at any point during a computation. It has been attracting increasing attention as it provides opportunities for low-power computation, being at the same time essential or eligible in various applications. In recent work, we have proposed a structural way of translating Reversing Petri Nets (RPNs) – a type of Petri nets that embeds reversible computation, to bounded Coloured Petri Nets (CPNs) – an extension of traditional Petri Nets, where tokens carry data values. Three reversing semantics are possible in RPNs: backtracking (reversing of the lately executed action), causal reversing (action can be reversed only when all its effects have been undone) and out of causal reversing (any previously performed action can be reversed). In this paper, we extend the RPN to CPN translation with formal proofs of correctness. Moreover, the possibility of introduction of cycles to RPNs is discussed. We analyze which type of cycles could be allowed in RPNs to ensure consistency with the current semantics. It emerged that the most interesting case related to cycles in RPNs occurs in causal semantics, where various interpretations of dependency result in different net’s behaviour during reversing. Three definitions of dependence are presented and discussed.

Expressiveness and analysis of Delayable Timed Petri Net*

We consider an extension of Timed Petri Nets “à la Ramchandani” where the transitions are partitioned into delayable and non-delayable transitions which has proven to be suitable for the design of synchronous circuits. For this model called Delayable Timed Petri Net (DTPN), the firing delay of a non-delayable transition is strict whereas a delayable transition can miss its firing delay. Since the delays are natural numbers, this model can be studied as a discrete time model.We deal with the expressiveness of DTPN by a comparison with the well known Merlin's Time Petri Net model for which transitions can fire in a time interval. We show that DTPN are strictly more expressive w.r.t. weak timed bisimilarity than Merlin's model under the discrete-time semantics. We then deal with the symbolic reachability analysis of DTPN, for which we show the complexity of the successor symbolic state computation to be O(n). In addition, we propose a reduction of the number of edges to explore that preserves the markings and the firing sequences. The symbolic state space exploration is implemented in a prototype tool, which is evaluated on a classical TPN problem and a circuit design application.

Overapproximation of the Number of Active Timers in Timed-Arc Petri Nets Using DP-Systems

Timed-arcs Petri nets are a time extension of Petri nets that allows assigning clocks to tokens. System of dynamic points on a metric graph (DP-systems) is another dynamical model that is studied in discrete geometry dynamics; DP-system combines continuous time and discrete branching events and used, for example, in study of localized Gaussian wave packets scattering on thin structures. In recent works, asymptotic estimates of the growth of the number of points in dynamic systems on metric graphs were obtained. In this paper, we provide a mean to overapproximate the number of different values of timers for a subclass of timed-arc Petri nets by constructing a system of dynamic points on a metric graph and prove overapproximation of the number of timer values by the number of points in the system of dynamic points.

Solving reachability problems on data-aware workflows

Recent advances in the field of Business Process Management (BPM) have brought about several suites able to model data objects along with the traditional control flow perspective. Nonetheless, when it comes to formal verification there is still a lack of effective verification tools on imperative data-aware process models and executions: the data perspective is often abstracted away and verification tools are often missing.Automated Planning is one of the core areas of Artificial Intelligence where theoretical investigations and concrete and robust tools have made possible the reasoning about dynamic systems and domains. Moreover planning techniques are gaining popularity in the context of BPM. Starting from these observations, we provide here a concrete framework for formal verification of reachability properties on an expressive, yet empirically tractable class of data-aware process models, an extension of Workflow Nets. Then we provide a rigorous mapping between the semantics of such models and that of three important Automated Planning paradigms: Action Languages, Classical Planning, and Model-Checking. Finally, we perform a comprehensive assessment of the performance of three popular tools supporting the above paradigms in solving reachability problems for imperative data-aware business processes, which paves the way for a theoretically well founded and practically viable exploitation of planning-based techniques on data-aware business processes.

Multiscale Microtubule Dynamics in Active Nematics.

In microtubule-based active nematics, motor-driven extensile motion of microtubule bundles powers chaotic large-scale dynamics. We quantify the interfilament sliding motion both in isolated bundles and in a dense active nematic. The extension speed of an isolated microtubule pair is comparable to the molecular motor stepping speed. In contrast, the net extension in dense 2D active nematics is significantly slower; the interfilament sliding speeds are widely distributed about the average and the filaments exhibit both contractile and extensile relative motion. These measurements highlight the challenge of connecting the extension rate of isolated bundles to the multimotor and multifilament interactions present in a dense 2D active nematic. They also provide quantitative data that is essential for building multiscale models.

Modelling the Process of Production of Diesel Fuels by the Use of Generalized Nets

The process of commodity diesel fuel production in a refinery has been modelled by the use of the Generalized Net (GN) apparatus. GNs are extensions of Petri nets and of all their modifications and extensions. The model accounts for the orders of different grades of diesel fuel and the available amounts of the different diesel fuel components. It can be used for the synchronization and optimization of these processes.

Interpreted synchronous extension of time Petri nets

Our work is integrated into a global methodology to design synchronously executed embedded critical systems. It is used for the development of medical devices implanted into human body to perform functional electrical stimulation solutions (used in pacemakers, deep brain stimulation...). These systems are of course critical and real time, and the reliability of their behaviors must be guaranteed. These medical devices are implemented into a programmable logic circuit in a synchronous way, which allows efficient implementation (space, consumption and actual parallelism of tasks execution). This paper presents a solution that helps to prove that the behavior of the implemented system respects a set of properties, using Petri nets for modeling and analysis purposes. But one problem in formal methods is that the hardware target and the implementation strategy can have an influence on the execution of the system, but is usually not considered in the modeling and verification processes. Resolving this issue is the goal of this article. Our work has two main results: an operational one, and a theoretical one. First, we can now design critical controllers with hard safety or real time constraints, being sure the behavior is still guaranteed during the execution. Second, this work broadens the scope of expressivity and analyzability of Petri nets extensions. Until then, none managed in the same formalism, both for modeling and analysis, all the characteristics we have considered (weights on arcs, specific test and inhibitor arcs, interpretation, and time intervals, including the management of effective conflicts and the blocking of transitions).

Rents, Experiments, and the Perpetual Presence of Concessionary Weather Insurance

Geographers have interpreted the rise of weather insurance for small agricultural producers as emblematic of financialization’s inexorable march to capitalize the countryside. Yet this market has proved far less successful than advocates hoped or critics feared. Rather than a speculative tool for surplus extraction from smallholders or a mechanism for their financial subjectification, this article reinterprets weather insurance as an infrastructure of concessionary transfers from the development sector to make market-mediated mechanisms work. These transfers are emblematic of the new distributional terms struck between donors, states, and insurance capital as financial risk transfer is articulated with the extension of fragmentary safety nets. Economic field experiments with insurance have proliferated as venues in which the value of insurance is tested by both economists and experimenting subjects. Just as data from these trials have suggested some positive welfare impacts, they have also indicated target clients are unwilling or unable to pay full market price, thus performing a new justification for the perpetual presence of subsidies. Such transfers present opportunities for reinsurers to command rents through their control of large pools of capital and their interpretive authority over techniques for pricing risk under uncertainty. In a changing climate, reinsurers are poised to collect larger rents from donors’ and governments’ premium subsidies meant to decrease insurance costs for the vulnerable. These dynamics of rent cycling underscore the urgency of building more equitable, systematic risk-sharing infrastructures to replace the current fragmentary archipelagos of weather insurance.

Bisognano–Wichmann Property for Rigid Categorical Extensions and Non-local Extensions of Conformal Nets

Given an (irreducible) Mobius covariant net $\mathcal A$, we prove a Bisognano-Wichmann theorem for its categorical extension $\mathscr E^{\textrm{d}}$ associated to the braided $C^*$-tensor category $\textrm{Rep}^{\textrm{d}}(\mathcal A)$ of dualizable (more precisely "dualized") Mobius covariant $\mathcal A$-modules. As a closely related result, we prove a (modified) Bisognano-Wichmann theorem for any (possibly) non-local extension of $\mathcal A$ obtained by a $C^*$-Frobenius algebra $Q$ in $\textrm{Rep}^{\textrm{d}}(\mathcal A)$. As an application, we discuss the relation between the domains of modular operators and the preclosedness of certain unbounded operators in $\mathscr E^{\textrm{d}}$.

Object-Centric Replay-Based Conformance Checking: Unveiling Desire Lines and Local Deviations

Conformance checking methods diagnose to which extent a real system, whose behavior is recorded in an event log, complies with its specification model, e.g., a Petri net. Nonetheless, the majority of these methods focus on checking isolated process instances, neglecting interaction between instances in a system. Addressing this limitation, a series of object-centric approaches have been proposed in the field of process mining. These approaches are based on the holistic analysis of the multiple process instances interacting in a system, where each instance is centered on the handling of an object. Inspired by the object-centric paradigm, this paper presents a replay-based conformance checking method which uses a class of colored Petri nets (CPNs) -- a Petri net extension where tokens in the model carry values of some types (colors). Particularly, we consider conservative workflow CPNs which allow to describe the expected behavior of a system whose components are centered on the end-to-end processing of distinguishable objects. For describing a system’s real behavior, we consider event logs whose events have sets of objects involved in the execution of activities. For replay, we consider a jump strategy where tokens absent from input places of a transition to fire move from their current place of the model to the requested places. Token jumps allow to identify desire lines, i.e., object paths unforeseen in the specification. Also, we introduce local diagnostics based on the proportion of jumps in specific model components. The metrics allow to inform the severity of deviations in precise system parts. Finally, we report experiments supported by a prototype of our method. To show the practical value of our method, we employ a case study on trading systems, where orders from users are matched to trade.

A Formal Approach to Requirements Engineering of Automated Systems: Facing the Challenge for New Automated Systems

It is a consensus that intelligent manufacturing plants should be automated, especially in what concerns automated processes to Industry 4.0. This new manufacturing approach is based on multifunctional distributed systems that, for its turn, depend on a sound design requirements phase. Consequently, the requirement specifications became even more significant in the design of intelligent manufacturing systems, where the possibility to analyze requirements previously could save time and effort. Frequently, relevant requirements assumptions change during the engineering process due to emergent and volatile requirements—called “scope creep.” A revision of the requirements approach should be demanding to minimize this problem. The proposal presented in this work anticipates the formal representation of automated systems requirements to allow the proper analysis and validation. Also, since conventional production lines have been replaced by a product-service (production) systems (PSS), there is pressure to review the requirements phase, mainly to automated systems. To increase the accuracy, we propose a requirements cycle composed of modeling, analysis, and (formal) verification where formalization is anticipated by capturing visual modeled requirements. Alternative approaches to the functional method are also explored, considering the Goal-oriented Requirements Engineering approach, the best fit to PSS. A formal process to treat requirements in a functional approach, represented by UML diagrams, is transferred to Petri Nets and submitted to formal analysis. Traditional translation from UML to Petri Nets is replaced by an object-oriented match to Petri Nets extensions covered by the standard ISO/IEC 15.909. A comparison between this approach and the goal-oriented raises a discussion about the requirements efficiency dilemma, where functionality could be pointed as the main reason to scope creep. Therefore, a strictly functional approach is proposed with a new transference algorithm, and the results are used to support the discussion about using goal-oriented alternatives. A case study of the chemical industry illustrates the practical use of the proposal.

A Petri net extension for systems of concurrent communicating agents with durable actions

This paper provides a true-concurrency approach for the specification and verification of systems of concurrent communicating agents with durable actions. We present high-level Petri nets with durable actions (DaHL) to cope with various details in such complex systems. We define a DaHL module as an open variant of time-dependent colored Petri nets. A DaHL system is a fused set of modules for systems consisting of concurrent agents which can interact with each other. We also introduce hybrid-based reachability graph that covers the entire state space of DaHL systems with a true-concurrency semantics. We show that such reachability graph allows us to check important properties such as deadlock-freeness, liveness, home space, and reversibility, and also to predict timing properties prior to real implementation. A case study is used to model and analyze a simple scenario where autonomous vehicles are able to transport containers freely in an enterprise environment.

Emplacement of “exotic” Zechstein slivers along the inverted Sontra Graben (northern Hessen, Germany): clues from balanced cross sections and geometrical forward modeling

Abstract. Lens-shaped slivers of Permian (Zechstein) amid Triassic units appearing along the master fault of the Sontra Graben in central Germany on the southern margin of the Central European Basin System (CEBS) were studied by means of detailed map analysis, a semi-quantitative forward model, and two balanced cross sections. We show how partial reactivation of the graben's main normal fault and shortcut thrusting in the footwall during inversion, combined with a specific fault geometry involving flats in low-shear-strength horizons, can produce the observed slivers of “exotic” Zechstein. This conceptual model implies that the Sontra Graben was created by about 1200 m of extension followed by some 1000 m of contraction, resulting in the few hundred meters of net extension observed today. Gentle dips and comparatively extensive exposure of some slivers suggest they are backthrust onto the reactivated normal fault's hanging wall, an interpretation corroborated in one location by shallow drilling. Backthrusting appears to have wedged some Zechstein slivers into incompetent Triassic units of the hanging wall. Based on regional correlation, extension most likely occurred in Late Triassic to Early Cretaceous time, while the contraction is almost certainly of Late Cretaceous age. The main aim of this paper is to describe an uncommon structural feature that we interpret to originate from inversion tectonics in an evaporite-bearing succession with multiple detachment horizons but without the presence of thick salt.