Class Of Nets Research Articles

Taking Complete Finite Prefixes To High Level, Symbolically*

Unfoldings are a well known partial-order semantics of P/T Petri nets that can be applied to various model checking or verification problems. For high-level Petri nets, the so-called symbolic unfolding generalizes this notion. A complete finite prefix of a P/T Petri net’s unfolding contains all information to verify, e.g., reachability of markings. We unite these two concepts and define complete finite prefixes of the symbolic unfolding of high-level Petri nets. For a class of safe high-level Petri nets, we generalize the well-known algorithm by Esparza et al. for constructing small such prefixes. We evaluate this extended algorithm through a prototype implementation on four novel benchmark families. Additionally, we identify a more general class of nets with infinitely many reachable markings, for which an approach with an adapted cut-off criterion extends the complete prefix methodology, in the sense that the original algorithm cannot be applied to the P/T net represented by a high-level net.

On the Complexity of Proving Polyhedral Reductions

We propose an automated procedure to prove polyhedral abstractions (also known as polyhedral reductions) for Petri nets. Polyhedral abstraction is a new type of state space equivalence, between Petri nets, based on the use of linear integer constraints between the marking of places. In addition to defining an automated proof method, this paper aims to better characterize polyhedral reductions, and to give an overview of their application to reachability problems. Our approach relies on encoding the equivalence problem into a set of SMT formulas whose satisfaction implies that the equivalence holds. The difficulty, in this context, arises from the fact that we need to handle infinite-state systems. For completeness, we exploit a connection with a class of Petri nets, called flat nets, that have Presburger-definable reachability sets. We have implemented our procedure, and we illustrate its use on several examples.

Event-Based Modeling of Input Signal Behaviors for Discrete-Event Controllers

Controllers for discrete-event systems are commonly designed using state-based formalisms, like state diagrams and Petri nets. These formalisms are strongly supported by the concept of events, which, from an automation system perspective, can be associated with a simple change in the value of a signal or more complex behavioral evolutions of the signals. In this paper, the characterization of several types of events is proposed, associated with different types of signals, such as Boolean and multivalued signals. The major goal of this characterization is to improve the compactness of the model, benefiting the editing and visual interpretation of the graphical model but keeping precise execution semantics, which in turn allows for the use of computational tools covering the different stages of system development. The behavioral model of the controller is produced using a non-autonomous class of Petri nets, the IOPT nets, and the associated IOPT-Tools, which supports the specification, simulation, property verification, and automatic code generation ready to be deployed into implementation platforms. All the types of proposed events have a behavioral sub-model executed concurrently with the main model of the controller. An application example is provided to illustrate some of the advantages of the adoption of the proposed approach, encapsulating the behavioral dependencies on the evolution of input signals into events.

Notes on noncommutative ergodic theorems

Given a semifinite von Neumann algebra M \mathcal M equipped with a faithful normal semifinite trace τ \tau , we prove that the spaces L 0 ( M , τ ) L^0(\mathcal M,\tau ) and R τ \mathcal R_\tau are complete with respect to pointwise—almost uniform and bilaterally almost uniform—convergences in L 0 ( M , τ ) L^0(\mathcal M,\tau ) . Then we show that the pointwise Cauchy property for a special class of nets of linear operators in the space L 1 ( M , τ ) L^1(\mathcal M,\tau ) can be extended to pointwise convergence of such nets in any fully symmetric space E ⊂ R τ E\subset \mathcal R_\tau , in particular, in any space L p ( M , τ ) L^p(\mathcal M,\tau ) , 1 ≤ p > ∞ 1\leq p>\infty . Some applications of these results in the noncommutative ergodic theory are discussed.

A descriptive review of next-generation insecticide-treated bed nets for malaria control

To date, insecticide-treated bed nets are the most effective tool in preventing malaria-related morbidity and mortality. All distributed bed nets contain pyrethroid insecticides; however, widespread resistance to this class in the malaria vectors, Anopheles spp., has led to the development of dual active ingredient bed nets, termed ‘next-generation bed nets’. These nets combine pyrethroids with a second chemistry, aimed at countering pyrethroid resistance. The World Health Organization (WHO) recently issued recommendations for three classes of next-generation bed nets. In this review, we report on key indicators across Africa for each net type. The results underscore a substantial variation in key indicators across Africa when comparing next-generation bed nets to traditional pyrethroid-only nets. Nevertheless, dual active ingredient bed nets generally outperform pyrethroid-only nets in a various settings. The results show that new nets are a formidable tool in malaria control, with superior performance compared to traditional pyrethroid-only nets. The variability in outcomes across Africa underscores the need for a region-specific approach, fostering a targeted and adaptive strategy for the deployment of these next-generation interventions.

Verification of Unary Communicating Datalog Programs

We study verification of reachability properties over Communicating Datalog Programs (CDPs), which are networks of relational nodes connected through unordered channels and running Datalog-like computations. Each node manipulates a local state database (DB), depending on incoming messages and additional input DBs from external services. Decidability of verification for CDPs has so far been established only under boundedness assumptions on the state and channel sizes, showing at the same time undecidability of reachability for unbounded states with only two unary relations or unbounded channels with a single binary relation. The goal of this paper is to study the open case of CDPs with bounded states and unbounded channels, under the assumption that channels carry unary relations only. We discuss the significance of the resulting model and prove the decidability of verification of variants of reachability, captured in fragments of first-order CTL. We do so through a novel reduction to coverability problems in a class of high-level Petri Nets that manipulate unordered data identifiers. We study the tightness of our results, showing that minor generalizations of the considered reachability properties yield undecidability of verification, both for CDPs and the corresponding Petri Net model.

Supervisor Synthesis for Petri Nets With Uncontrollable and Unobservable Transitions

This paper focuses on designing event feedback supervisors to enforce control specifications on Petri nets with uncontrollable and unobservable transitions. For each observation, the supervisor is able to select some controllable transitions to disable such that the system never reaches illegal markings. Two different methods are given to design such a supervisor. The first method computes the control policy by solving some integer linear programming problems, while the second one designs supervisors by taking advantage of the structural properties of a class of Petri nets. The computational efficiencies of these two methods increase successively at the expense of their application scopes. Two examples are given to illustrate the proposed methods, respectively. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The motivation of this paper consists in ensuring the behavior of a manufacturing system within a given legal behavior. The typical task for a designer is to design a supervisor to restrict that the system never reaches a forbidden state under limited control and observation ability. To this end, this paper proposes two different methods to design such a supervisor. The first one needs to solve integer linear programming problems, while the second one is based on the structural analysis of a special class of systems. It should be noted that although the application scope of the first method is wider, the second method has higher computational efficiency. Therefore, the suitable method can be chosen in accordance with the specific application scenario, which is significant and useful to manufacturing engineers.

Modular rewritable Petri nets: An efficient model for dynamic distributed systems

Modern distributed systems are becoming pervasive and increasingly provided with adaptation, (self-)reconfiguration and mobility capability. On one side, to face the challenges of the highly dynamic environments where they are deployed. On the other side, to keep production/maintenance costs down. Therein lies the increasing demand for formal models encompassing all of these aspects (besides concurrency). Hardly any of the classical formalisms like Petri Nets, Automata, and Process Algebra, even though powerful, permits designers to easily specify dynamic structural changes to systems and evaluate their impact on system behaviour. That has led to several extensions of classical formal models (e.g., the Pi calculus or the Nets-within-Nets paradigm) rarely accompanied by suitable analysis techniques. A recent formalization of a class of Rewritable Place-Transition Nets (RwPT) in Maude has proved potentially convenient to specify dynamically reconfigurable systems. Concerning analogous proposals, the RwPT formalism provides more abstraction/flexibility in modelling and efficiency in analysis. Nevertheless, its ability to scale the size of distributed systems built of several similar (nested) components is limited.This paper presents a compositional approach to define large RwPT models in a typical algebraic way and to exploit the modular structure of models during the analysis: Symmetries are implicitly captured by composite node-labelling (reflecting the model's hierarchical structure) that is preserved by net rewrites. A distributed, gracefully degrading production system is used as a case study. Experimental evidence points out the dramatic impact of the approach against a non-modular one and the advantages over alternative techniques. Even if the emphasis is on state-space-based verification, the paper shows the convenience of combining it with structural analysis, which is typical of Petri nets as well. For that purpose, rewrite-rule abstractions are given in the form of guidelines.

Bio-efficacy of field aged novel class of long-lasting insecticidal nets, against pyrethroid-resistant malaria vectors in Tanzania: A series of experimental hut trials.

New classes of long-lasting insecticidal nets (LLINs), have been recommended by the World Health Organization (WHO) to control malaria vectors resistant to pyrethroid insecticides. This study was nested in a large-scale cluster-randomized controlled trial conducted (cRCT) in Tanzania. A series of experimental hut trials (EHTs) aimed to evaluate the bio-efficacy of trial LLINs on mosquito indicators most pertinent to malaria transmission over 3 years of use in the community in order to better understand the outcomes of the cRCT. The following field-collected LLINs were assessed: 1) Olyset Plus (combining piperonyl butoxide synergist and permethrin), 2) Interceptor G2 (chlorfenapyr and alpha-cypermethrin), 3) Royal Guard (pyriproxyfen and alpha-cypermethrin), 4) Interceptor (alpha-cypermethrin only) conducted in parallel with 5) a new Interceptor, and 6) an untreated net. Thirty nets of each type were withdrawn from the community at 12, 24, and 36 months after distribution and used for the EHTs. Pre-specified outcomes were 72-hour mortality for Interceptor G2, 24-hour mortality for Olyset Plus, and fertility based on egg development stage for Royal Guard. Overall, Interceptor G2 LLINs induced higher 72-hour mortality compared to standard LLINs of the same age up to12 months (44% vs 21%, OR: 3.5, 95% CI: 1.9-6.6, p-value < 0.001), and 24-hour mortality was only significantly higher in Olyset Plus when new (OR: 13.6, 95%CI: 4.4-41.3, p-value < 0.001) compared to standard LLINs but not at 12 months (17% vs 13%; OR: 2.1, 95% CI: 1.0-4.3; p-value = 0.112). A small, non-significant effect of pyriproxyfen on Anopheles fertility was observed for Royal Guard up to 12 months (75% vs 98%, OR: 1.1, 95% CI: 0.0-24.9, p-value = 0.951). There was no evidence of a difference in the main outcomes for any of the new classes of LLINs at 24 and 36 months compared to standard LLINs. Interceptor G2 LLINs showed superior bio-efficacy compared to standard LLINs only up to 12 months, and the effect of Olyset Plus was observed when new for all species and 12 months for An. gambiae s.l. only. The pyriproxyfen component of Royal Guard had a short and limited effect on fertility. The decrease in effectiveness of Olyset Plus and Royal Guard LLINs in the EHTs aligns with findings from the cRCT, whereas efficacy of Interceptor G2 lasted for a longer period in the cRCT compared to the EHT. Further investigations are needed to understand the complete scope of chlorfenapyr mode of action. Additional EHT in various contexts will help confirm the residual efficacy of the dual active ingredient LLINs and support the development of longer-lasting nets.

Duality of controllability and observability in proportional equal conflict timed continuous Petri Nets

Controllability and observability properties have been widely studied in Timed Continuous Petri Nets (TCPNs), a class of piecewise affine systems, in order to analyze and control crowded discrete event systems. This work studies the concept of duality applied to TCPNs as a vehicle to establish links between controllability and observability, i.e., a synergy to improve the understanding of these properties and to enlarge the class of nets that can be analyzed. To achieve this, we study the concepts of rank-controllability and rank-observability. They capture structural conditions for controllability and observability. Afterwards, the computation of dual nets for Fork-Attribution (FA), Choice-Free (CF), Join-Free (JF), and Proportional Equal Conflict (PEQ) TCPNs subclasses are presented. By using the dual definition, several relations between the primal’s controllability and its dual’s observability are stated. Particularly, in FA rank-controllability and rank-observability are dual properties. In consistent and strongly connected CF, JF, and PEQ nets, the rank-observability of the dual is sufficient for the rank-controllability of the primal. The opposite implication holds for CF and PEQ if the self-loop places, added by the dual construction methodology, are measurable.

Adaptive supervisory control for a class of Petri nets with bimodal transitions

Adaptive supervisory control for a class of Petri nets with bimodal transitions

On the Complexity of Techniques That Make Transition Systems Implementable by Boolean Nets

Let us consider some class of (Petri) nets. The corresponding Synthesis problem consists in deciding whether a given labeled transition system (TS) A can be implemented by a net N of that class. In case of a negative decision, it may be possible to convert A into an implementable TS B by applying various modification techniques, like relabeling edges that previously had the same label, suppressing edges/states/events, etc. It may however be useful to limit the number of such modifications to stay close to the original problem, or optimize the technique. In this paper, we show that most of the corresponding problems are NP-complete if the considered class corresponds to so-called flip-flop nets or some flip-flop net derivatives.

Effectiveness of long-lasting insecticidal nets with pyriproxyfen–pyrethroid, chlorfenapyr–pyrethroid, or piperonyl butoxide–pyrethroid versus pyrethroid only against malaria in Tanzania: final-year results of a four-arm, single-blind, cluster-randomised trial

New classes of long-lasting insecticidal nets (LLINs) containing two active ingredients have been recently recommended by WHO in areas where malaria vectors are resistant to pyrethroids. This policy was based on evidence generated by the first 2 years of our recently published trial in Tanzania. In this Article, we report the final third-year trial findings, which are necessary for assessing the long-term effectiveness of new classes of LLIN in the community and the replacement intervals required. A third year of follow-up of a four-arm, single-blind, cluster-randomised controlled trial of dual active ingredient LLINs was conducted between July 14, 2021, and Feb 10, 2022, in Misungwi, Tanzania. Restricted randomisation was used to assign 84 clusters to the four LLIN groups (1:1:1:1) to receive either standard pyrethroid (PY) LLINs (reference), chlorfenapyr-PY LLINs, pyriproxyfen-PY LLINs, or piperonyl butoxide (PBO)-PY LLINs. All households received one LLIN for every two people. Data collection was done in consenting households in the cluster core area with at least one child between 6 months and 15 years of age who permanently resided in the selected household. Exclusion criteria were householders absent during the visit, living in the cluster buffer area, no adult caregiver capable of giving informed consent, or eligible children who were severely ill. Field staff and study participants were masked to allocation, and those analysing data were not. The primary 24-month endpoint was reported previously; here, we present the secondary outcome, malaria infection prevalence in children at 36 months post LLIN distribution, reported in the intention-to-treat analysis. The trial was registered with ClinicalTrials.gov (NCT03554616) and is now complete. Overall usage of study nets was 1023 (22·3%) of 4587 people at 36 months post distribution. In the standard PY LLIN group, malaria infection was prevalent in 407 (37·4%) of 1088 participants, compared with 261 (22·8%) of 1145 in the chlorfenapyr-PY LLIN group (odds ratio 0·57, 95% CI 0·38-0·86; p=0·0069), 338 (32·2%) of 1048 in the PBO-PY LLIN group (0·95, 0·64-1·42; p=0·80), and 302 (28·8%) of 1050 in the pyriproxyfen-PY LLIN group (0·82, 0·55-1·23; p=0·34). None of the participants or caregivers reported side-effects. Despite low coverage, the protective efficacy against malaria offered by chlorfenapyr-PY LLINs was superior to that provided by standard PY LLINs over a 3-year LLIN lifespan. Appropriate LLIN replacement strategies to maintain adequate usage of nets will be necessary to maximise the full potential of these nets. Department for International Development, UK Medical Research Council, Wellcome Trust, Department of Health and Social Care, and Bill & Melinda Gates Foundation via the Innovative Vector Control Consortium.

Discrete Isothermic Nets Based on Checkerboard Patterns

This paper studies the discrete differential geometry of the checkerboard pattern inscribed in a quadrilateral net by connecting edge midpoints. It turns out to be a versatile tool which allows us to consistently define principal nets, Koenigs nets and eventually isothermic nets as a combination of both. Principal nets are based on the notions of orthogonality and conjugacy and can be identified with sphere congruences that are entities of Möbius geometry. Discrete Koenigs nets are defined via the existence of the so-called conic of Koenigs. We find several interesting properties of Koenigs nets, including their being dualizable and having equal Laplace invariants. Isothermic nets can be defined as Koenigs nets that are also principal nets. We prove that the class of isothermic nets is invariant under both dualization and Möbius transformations. Among other things, this allows a natural construction of discrete minimal surfaces and their Goursat transformations.

PermaNet Dual, a new deltamethrin-chlorfenapyr mixture net, shows improved efficacy against pyrethroid-resistant Anopheles gambiae sensu lato in southern Benin

Pyrethroid-chlorfenapyr nets have demonstrated improved entomological and epidemiological impact in trials across Africa. This is driving increased demand for this novel net class in malaria-endemic countries. PermaNet Dual is a new deltamethrin-chlorfenapyr net developed by Vestergaard Sàrl to provide more options to malaria control programmes. We performed an experimental hut trial to evaluate the efficacy of PermaNet Dual against wild, free-flying pyrethroid-resistant Anopheles gambiae sensu lato in Covè, Benin. PermaNet Dual induced superior levels of mosquito mortality compared to a pyrethroid-only net and a pyrethroid-piperonyl butoxide net both when unwashed (77% with PermaNet Dual vs. 23% with PermaNet 2.0 and 56% with PermaNet 3.0, p < 0.001) and after 20 standardised washes (75% with PermaNet Dual vs. 14% with PermaNet 2.0 and 30% with PermaNet 3.0, p < 0.001). Using a provisional non-inferiority margin defined by the World Health Organisation, PermaNet Dual was also non-inferior to a pyrethroid-chlorfenapyr net that has demonstrated improved public health value (Interceptor G2), for vector mortality (79% vs. 76%, OR = 0.878, 95% CIs 0.719–1.073) but not for blood-feeding protection (35% vs. 26%, OR = 1.424, 95% CIs 1.177–1.723). PermaNet Dual presents an additional option of this highly effective net class for improved control of malaria transmitted by pyrethroid-resistant mosquitoes.

On Liveness Enforcement of Distributed Petri Net Systems

In this paper, we consider the liveness enforcement problem in a class of Petri nets (PN) modeling distributed systems. They are called <i>synchronized sequential processes</i> (SSP). The presented design algorithm is based on the construction of a control PN, an abstraction of the relations of the T-semiflows, and buffers of the original nonstructurally live PN. The <i>control PN</i> evolves in parallel with the system, avoiding the firing of transitions that may lead the system to non liveness. Four algorithms are presented, one allowing for the computation of the control PN and three ensuring its liveness.

Soundness-preserving composition of synchronously and asynchronously interacting workflow net components

In this paper, we propose a compositional approach to constructing correct formal models of information systems from correct models of interacting components. Component behavior is represented using workflow nets — a class of Petri nets. Interactions among components are encoded in an additional interface net. The proposed approach is used to model and compose synchronously and asynchronously interacting workflow nets. Using Petri net morphisms and their properties, we prove that the composition of interacting workflow nets preserves the correctness of components and of an interface.

Symmetry‐Enforced 2D Hourglass Phononic Nodal Net

Topological nodal‐line semimetals have received extensive attention in recent years, and they exhibit a variety of shapes under various crystallographic symmetry protections, including nodal rings, nodal chains, and nodal knots. By using symmetry analysis and an effective force constant model, it is proposed that a class of 2D hourglass nodal nets protected by nonsymmorphic symmetry can exist in the space group , where the glide operations play a crucial role in the formation of the nets. Further effective model analysis shows that the connect points of the nets are Dirac points that are forced by the symmetries. Based on first‐principle calculations, it is predicted that this nodal net can be realized in the phonon dispersion of 3D Sn. The Berry phase and nontrivial surface states further support its nontrivial topological characteristics. Herein, the studies expand the nodal structure in the study of nodal line in phononic systems and offer a solid foundation for subsequent experimental investigation on this challenging topological state.

Small-Size Liveness-Enforcing Supervisor for Automated Manufacturing Systems Using the Theory of Transition Cover

The supervisor simplification problem for automated manufacturing systems (AMSs) has been receiving increasing attention in recent years. This article uses a well-known class of Petri nets, namely, systems of sequential systems with shared resources (S4Rs) to model general AMSs. We aim to simplify the liveness-enforcing supervisor for S4R by using the concept of transition cover (TC). Deadlocks in S4R can be characterized by a kind of special structural object called perfect activity circuits (PACs). First, a set of special PACs are defined as a TC and its effectness is also verified. Then, by adding a monitor with a control variable to each PAC in an effective TC (ETC), we establish a liveness-enforcing supervisor for S4R. The control variables are determined by solving an integer linear programming problem so as to increase the supervisor’s permissiveness as much as possible. Under the proposed control methodology, it is analyzed that the upper bound of the number of monitors equates to that of transitions in S4R. Especially for the system with a few transitions, since not many monitors are added, the proposed supervisor has relatively small-scaled structures or a small number of control places. In addition, we present algorithms to get an ETC from any nonlive S4R. Based on this ETC, we can design one liveness-enforcing supervisor of small size for the underlying S4R. Finally, some examples are used to illustrate the proposed approach.

Robust Petri Net Controllers for Flexible Manufacturing Systems With Multitype and Multiunit Unreliable Resources

It is inevitable that resource failures occur in real production processes, and sometimes many different types of unreliable resource failures may occur. Once there are resource failures, the stagnation states of production caused by these failures, called as failure blockings (FBs), tend to appear. Hence, both deadlocks and FBs can arise to reduce production efficiency sharply. Designing robust control policies for such an automated system is thus very important. Our work focuses on a novel robust Petri net controller of flexible manufacturing systems with multitype and multiunit of unreliable resources. First, under the assumption that all resources are reliable, these systems are modeled by a class of Petri nets called systems of simple sequential processes with resources (S3PRs). For each operation place that is a holder of an unreliable resource, the corresponding repair place and related transitions are added to the net and an S3PR with unreliable resources (S3PRu) is developed. For an S3PRu, the formal definition of FBs is then proposed. Such an FB is characterized by a maximal perfect resource-transition circuit (MPC). Next, the concept of a critical set of MPCs is introduced. For any two adjacent MPCs in such a critical set, one input transition of the former and one output transition of the latter are connected by passing through resource places. A <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\xi $ </tex-math></inline-formula> -resource is a one-unit resource shared by two or more MPCs that do not contain each other. For an S3PRu without <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\xi $ </tex-math></inline-formula> -resources and critical sets of MPCs, a control place corresponding to an MPC is added to the net with its output arcs to the input transitions of the MPC. However, for an S3PRu with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\xi $ </tex-math></inline-formula> -resources or critical sets of MPCs, the output arcs of each control place are added to the source transitions of the original net. Thus, a novel robust controller of an S3PRu is synthesized. Such a robust controller can guarantee that as long as at least one unit of each type of unreliable resources can work normally, all kinds of parts can be processed to complete smoothly their tasks through any one of their process routes. Finally, three examples are provided to illustrate the efficiency of the proposed robust controller.