Extension Of Nets Research Articles

Context-free commutative grammars with integer counters and resets

We study the computational complexity of reachability, coverability and inclusion for extensions of context-free commutative grammars with integer counters and reset operations on them. Those grammars can alternatively be viewed as an extension of communication-free Petri nets. Our main results are that reachability and coverability are inter-reducible and both NP-complete. In particular, this class of commutative grammars enjoys semi-linear reachability sets. We also show that the inclusion problem is, in general, coNEXP-complete and already Π2P-complete for grammars with only one non-terminal symbol. Showing the lower bound for the latter result requires us to develop a novel Π2P-complete variant of the classic subset sum problem.

Supercyclidic Nets

Supercyclides are surfaces with a characteristic conjugate parametrization consisting of two families of conics. Patches of supercyclides can be adapted to a Q-net (a discrete quadrilateral net with planar faces) such that neighboring surface patches share tangent planes along common boundary curves. We call the resulting patchworks 'supercyclidic nets' and show that every Q-net in $\mathbb{R}P^3$ can be extended to a supercyclidic net. The construction is governed by a multidimensionally consistent 3D system. One essential aspect of the theory is the extension of a given Q-net in $\mathbb{R}P^N$ to a system of circumscribed discrete torsal line systems. We present a description of the latter in terms of projective reflections that generalizes the systems of orthogonal reflections which govern the extension of circular nets to cyclidic nets by means of Dupin cyclide patches.

Modeling Self-Adaptive Software Systems With Learning Petri Nets

Traditional models unable to model adaptive software systems since they deal with fixed requirements only, but cannot handle the behaviors that change at runtime in response to environmental changes. In this paper, an adaptive Petri net (APN) is proposed to model a self-adaptive software system. It is an extension of hybrid Petri nets by embedding a neural network algorithm into them at some special transitions. The proposed net has the following advantages: 1) it can model a runtime environment; 2) the components in the model can collaborate to make adaption decisions while the system is running; and 3) the computation is done at the local component, while the adaption is for the whole system. We illustrate the proposed APN by modeling a manufacturing system.

An Upper Bound for the Reachability Problem of Safe, Elementary Hornets

In this paper we study the complexity of the reachability problem HORNETS, an algebraic extension of object nets. Here we consider the restricted class of safe, elementary HORNETS. In previous work we established the lower bound, i.e. reachability requires at least exponential space. In another work we have shown we can simulate elementary HORNETS with elementary object nets EOS, where reachability is known to be PSpace-complete. Since this simulation leads to a double exponential increase in the size of the simulating EOS, we obtain that for HORNETS the reachability problem is solvable in double exponential space. In this contribution we show that this kind of simulation is rather bad, since we show that exponential space is sufficient. Together with the known lower bound this shows that the upper is tight.

Differential regulation of apical-basolateral dendrite outgrowth by activity in hippocampal neurons.

Hippocampal pyramidal neurons have characteristic dendrite asymmetry, characterized by structurally and functionally distinct apical and basolateral dendrites. The ability of the neuron to generate and maintain dendrite asymmetry is vital, since synaptic inputs received are critically dependent on dendrite architecture. Little is known about the role of neuronal activity in guiding maintenance of dendrite asymmetry. Our data indicate that dendrite asymmetry is established and maintained early during development. Further, our results indicate that cell intrinsic and global alterations of neuronal activity have differential effects on net extension of apical and basolateral dendrites. Thus, apical and basolateral dendrite extension may be independently regulated by cell intrinsic and network neuronal activity during development, suggesting that individual dendrites may have autonomous control over net extension. We propose that regulated individual dendrite extension in response to cell intrinsic and neuronal network activity may allow temporal control of synapse specificity in the developing hippocampus.

Lending Petri nets

We study Lending Petri nets, an extension of Petri nets where places may carry a negative number of tokens. This allows for modeling contracts where a participant may promise to give some of her resources under the guarantee that some other resources will eventually be obtained in exchange. We then propose an interpretation of the Horn fragment of Propositional Contract Logic in Lending Petri nets. In particular, we show that provability in the logic corresponds to reachability of certain markings in nets, and that proof traces correspond to “honored” firing sequences in nets.

Morphological change in the Pearl River Delta, China

Morphological changes in the Pearl River Delta (PRD) have been investigated using bathymetric charts, underwater Digital Elevation Models, remote sensing data and Geographic Information Systems. Water depths were extracted from digitized charts to explore the accretion–erosion characteristics of three estuarine environments, and to provide quantitative estimates of changes in sediment volumes. Multi-temporal satellite images have been used, in combination with topographical data, to analyze the coastline changes. PRD has gained an abundant amount of sediment of almost 9.45 × 105 km3 above the 10-m isobath in the period roughly between 1970 and 2010; the average sedimentation rate was 3.15 × 104 km3/yr. Between 1976 and 2006, the coastline extended seaward by 579.2 m on average, with a mean net extension rate of 19.3 m/yr. The results suggest that the PRD experienced a major phase of accretion, with net erosion only in some local zones. Coastline extension, associated with major morphological changes, has accelerated in recent decades. Changes in boundary conditions, such as sea-level rise, seem to have relatively minor impacts on the dramatic changes in the morphology of the estuaries. The seaward extension of the coastlines shows an increasing trend whereas the sediment supply from the delta displays a decreasing trend. A detailed comparative analysis demonstrates that land reclamation in the PRD is the most significant factor that progressively alters the delta morphology, overwhelming the effects of subsidence and sediment supply.

Spatial–temporal evolution of aeolian blowout dunes at Cape Cod

This paper explores historical evolution of blowouts at Cape Cod National Seashore (CCNS), USA — a site that hosts one of the world's highest densities of active and stabilized blowouts. The Spatial–Temporal Analysis of Moving Polygons (STAMP) method is applied to a multi-decadal dataset of aerial photography and LiDAR to extract patterns of two-dimensional movement and morphometric changes in erosional deflation basins and depositional lobes. Blowout development in CCNS is characterized by several geometric (overlap) and movement (proximity) responses, including: i) generation and disappearance, ii) extension and contraction, iii) union or division, iv) clustering and v) divergence by stabilization. Other possible movement events include migration, amalgamation and proximal stabilization, but they were not observed in this study. Generation events were more frequent than disappearance events; the former were highest between 1985 and 1994, while the latter were highest between 2000 and 2005. High rates of areal change in erosional basins occurred between 1998 and 2000 (+3932m2a−1), the lowest rate (+333m2a−1) between 2005 and 2009, and the maximum rate (+4589m2a−1) between 2009 and 2011. Union events occurred mostly in recent years (2000–2012), while only one division was observed earlier (1985–1994). Net areal changes of lobes showed gradual growth from a period of contraction (−1119m2a−1) between 1998 and 2000 to rapid extension (+2030m2a−1) by 2010, which is roughly concurrent with rapid growth of erosional basins between 2005 and 2009. Blowouts extended radially in this multi-modal wind regime and, despite odd shapes initially, they became simpler in form (more circular) and larger over time. Net extension of erosional basins was toward ESE (109°) while depositional lobes extended SSE (147°). Lobes were aligned with the strongest (winter) sand drift vector although their magnitude of areal extension was only 33% that of the basins. These differences in extension responses likely result from more complex and evolving flow-form interactions inside erosional basins. Historical photographs and CCNS documents suggest that blowout evolution may be influenced by land-use changes, such as revegetation campaigns in 1985 that were followed by high blowout generation. High magnitude regional storm events (e.g., hurricanes) also play a role. The analytical framework presented provides a systematic means for two-dimensional geomorphic change detection and pattern analysis that can be applied to other landscapes.

Modelling and Analysis of Mobile Computing Systems: An Extended Petri Nets Formalism

In its basic version, Petri Nets are defined as fixed graphs, where the behaviour of the system is modelled as the marking of the graph which changes over time. This constraint makes the Petri Nets a poor tool to deal with reconfigurable systems as mobile computing systems, where the structure of the system can change as its behaviour, during time. Many extended Petri nets were proposed to deal with this weakness. The aim of this work is to present a new extension of Petri Nets, where the structure of the graph can be highly flexible. This flexibility gives a rich model with complex behaviours, not allowed in previous extensions. The second aim is to prove that even these behaviours are so complex; they can be translated into other low level models (as Coloured Petri Nets [21]) and so be analysed. This translation exploits Dynamic Petri Nets [11] as an intermediary representation between our model and Coloured Petri Nets.

SPN as a tool for risk modeling of fires in process industries

The modeling of risk to safety of personnel in process industries is very often carried out by the application of event trees. Event tree method is an inductive analysis that starts with a specified initiating event and ends up with the possible consequences of this event. Risk to safety of personnel is then defined as a product of event frequency and its consequences. However, event tree is a steady-state method. Given dynamic nature of industry processes, substitution of event trees for better suited modeling tool is necessary for accurate risk estimation. One such tool was found in a form of modeling language Petri Nets and its extensions, all capable of modeling dynamic processes. This article presents modeling the risk to safety of personnel on an offshore hydrocarbon production facility following hydrocarbon leak. As survival of personnel during hydrocarbon leak depends on numerous time-dependent events like fire escalation and gas cloud explosion, an extension of Petri Nets, Stochastic Petri Nets, was chosen as a suitable modeling tool. Event descriptions and model construction were based on realistic data from an offshore industry. Resulting probabilities of fatality following hydrocarbon leak were computed using Petri Nets module of GRIF software. Obtained probabilities were then compared with event tree and Direct Monte Carlo method results.

ω-Petri Nets: Algorithms and Complexity

We introduce ω-Petri nets ωPN, an extension of plain Petri nets with ω-labeled input and output arcs, that is well-suited to analyse parametric concurrent systems with dynamic thread creation. Most techniques such as the Karp and Miller tree or the Rackoff technique that have been proposed in the setting of plain Petri nets do not apply directly to ωPN because ωPN define transition systems that have infinite branching. This motivates a thorough analysis of the computational aspects of ωPN. We show that an ωPN can be turned into a plain Petri net that allows us to recover the reachability set of the ωPN, but that does not preserve termination an ωPN terminates iff it admits no infinitely long execution. This yields complexity bounds for the reachability, boundedness, place boundedness and coverability problems on ωPN. We provide a practical algorithm to compute a coverability set of the ωPN and to decide termination by adapting the classical Karp and Miller tree construction. We also adapt the Rackoff technique to ωPN, to obtain the exact complexity of the termination problem. Finally, we consider the extension of ωPN with reset and transfer arcs, and show how this extension impacts the decidability and complexity of the aforementioned problems.

Generalizing the Compositions of Petri Nets Modules

Modularity is a mandatory principle to apply Petri nets to real world-sized systems. Modular extensions of Petri nets allow to create complex models by combining smaller entities. They facilitate t...

Generalizing the Compositions of Petri Nets Modules

Modularity is a mandatory principle to apply Petri nets to real world-sized systems. Modular extensions of Petri nets allow to create complex models by combining smaller entities. They facilitate the modeling and verification of large systems by applying a divide and conquer approach and promoting reuse. Modularity includes a wide range of notions such as encapsulation, hierarchy and instantiation. Over the years, Petri nets have been extended to include these mechanisms in many different ways. The heterogeneity of such extensions and their definitions makes it difficult to reason about their common features at a general level. We propose in this article an approach to standardize the semantics of modular Petri nets formalisms, with the objective of gathering even the most complex modular features from the literature. This is achieved with a new Petri nets formalism, called the LLAMAS Language for Advanced Modular Algebraic Nets LLAMAS. We focus principally on the composition mechanism of LLAMAS, while introducing the rest of the language with an example. The composition mechanism is introduced both informally and with formal definitions. Our approach has two positive outcomes. First, the definition of new formalisms is facilitated, by providing common ground for the definition of their semantics. Second, it is possible to reason at a general level on the most advanced verification techniques, such as the recent advances in the domain of decision diagrams.

Simulation‐based optimisation of wastewater flow and composition for on‐site treatment in the food and beverage industry utilising reference nets in combination with genetic algorithms

AbstractThis study introduces the concept of computer modelling and simulation of complex bioprocesses and systems using an approach that combines the reference net formalism with machine learning and optimisation techniques. Reference nets are an extension of high level Petri Nets, which can be used as a central visualisation and modelling tool. The net‐in‐net paradigm used by reference nets makes it possible to model complex processes, such as those found in the food and beverage industry. A plugin/interface system based on the java programming language allows implementation of advanced mathematical modelling techniques at specific points in entire system simulations. Separate optimisation tools can also run and modify existing reference net models for fast solutions to efficiency problems. We present an example system that simulates a specific section of a beer brewery using the reference net formalism, which is optimised using a genetic algorithm. We show in detail how the different software packages can be combined for a simulation based optimisation approach. The optimisation technique specifically addresses the wastewater pollution load in regard to its chemical oxygen demand. A beer brewery was chosen as an example for this study due to the constantly increasing requirements to lower energy and water consumption in this industry. One possibility to lower the energy and water demands is to effectively treat wastewater produced by the brewery, which can introduce cost savings by providing recycled water and biogas. Most approaches to wastewater treatment are end‐of‐pipe solutions that do not consider the brewery as a whole. A brewery contains many processes that can be running concurrently and interacting with one another (e.g. brewing, clean‐in‐place and bottling) with each process producing varying amounts of wastewater with different pollution loads. Optimisation of the scheduling of the different processes with respect to the wastewater production will allow for more effective wastewater treatment, and therefore cost and energy savings. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Parametric multisingular hybrid Petri nets: Formal definitions and analysis techniques

Multisingular hybrid Petri net (MSHPN) is an extension of hybrid Petri nets enriched with the capabilities of hybrid automata to achieve the practical expressive power of multisingular hybrid automata. In this paper, we define parametric multisingular hybrid Petri nets (P-MSHPNs), as a parametric extension of MSHPNs. We present the parametric reachability analysis techniques and algorithms and prove that the parametric reachability analysis of P-MSHPNs amounts to the analysis of standard MSHPNs. Once the parametric state space of a P-MSHPNs model is computed, it can either be used for parametric model checking analysis using the existing techniques or be instantiated to obtain non-parametric state spaces. P-MSHPNs models can be analysed to obtain the set of feasible configurations for the system parameters. We also give a method for deriving the set of constraints on the parameters that ensure the correctness of an invariant property and a method for finding the optimum parameter configuration.

Modeling and analysis of memory virtualization in cloud computing

Virtualization is a promising approach to consolidating multiple online services onto a smaller number of computing resources. The adoption of virtualization and mappings between physical and virtual resources can further exacerbate challenges. Stochastic reward net (SRN) is an extension of stochastic Petri nets which provides compact modeling facilities for system analysis. In this paper, we address SRN hierarchical modeling of memory virtualization in cloud computing. Memory overcommit techniques such as ballooning, page swapping, and sharing, are applied and modeled for virtualization as a lower-level model. We propose three memory management policies, combination of ballooning and swapping intended for busy virtual memory (VMEM), to increase virtual memory utilization. These policies are handled by using guard functions of transition in SRN. The hypervisor with these policies can relinquish the memory pages of not so busy VMEM and let the busy VMEM get the pages. Memory availability with failure related behavior is modeled and analyzed as a upper-level model. We combine above two level models together and get performability measures. The upper-level model is the structure state model representing the state of the system with regard to failures and repairs of memory pages (banks). There are $$i$$ i active memory pages in progress. Each state of $$i$$ i is assigned a reward rate equal to the memory utilization from the lower-level performance model. The lower-level model captures the performance of the system, especially several memory utilization measures, within a given structure state. Measures of interest are considered as follows: memory utilization for allocated and actually used memory, memory availability with memory failure/repair behavior. These measures are expressed in terms of the expected values of reward rate functions for SRNs.

On the effective strain tensor in heterogeneous materials

This paper considers effective strain tensors within the context of linear elastic equilibrium theory. The elastic properties of structured materials are often averaged over subvolumes of various scales inside the material. For subvolumes smaller than a representative volume element, simple volume-averaging of the stress and strain may not preserve the elastic energy. We introduce an averaging process which preserves the energy for all boundary conditions. This averaging process emphasizes the parts of the material which carry the most stress. Here the effective strain is weighted by the local stress, and can be interpreted as an average strain over all paths taken by loads and forces through the volume. This alternative effective strain may be especially appropriate for materials with voids, such as foams and granular matter, as the averaging only involves the material itself. For uniform boundary conditions the weighted strain matches the volume-averaged strain. This paper investigates the properties of this weighted strain tensor. First, for each path taken by loads and forces through the volume we can measure a net length as well as a net extension due to the linear deformation. The weighted effective strain equals the ratio of average length to average extension, where the averaging is over all possible force paths. Thus this method provides a connection to load path analysis. Secondly, even when the average rotation within the subvolume is zero, there may be local fluctuations in the rotation field. These rotations can act like a mechanism, transferring elastic energy between boundaries or degrees of freedom. The effective strain defined here highlights this mechanism effect.

On the Complexity of the Reachability Problem for Safe, Elementary Hornets

In this paper we study the complexity of HORNETS, an algebraic extension of object nets. We define a restricted class: safe, elementary HORNETS, to guarantee finite state spaces. It will turn out, that the reachability problem for this class requires exponential space, which is a major increase when compared to safe, elementary object nets, which require polynomial space.

클라우드 시스템의 가상 스위치 모델링

Abstract Virtualization is a promising approach to consolidating multiple online services onto a smaller number of computing resources. A virtualized server environment allows computing resources to be shared among multiple performance isolated platforms called virtual machines. Through server virtualization software, applications servers are encapsulated into VMs, and deployed with APIs on top generalized pools of CPU and memory resources. Networking and security have been moved to a software abstraction layer that transformed computing, network virtualization. And it paves the way for enterprise to rapidly deploy networking and security for any application by creating the virtual network. Stochastic reward net (SRN) is an extension of stochastic Petri nets which provides compact modeling facilities for system analysis. In this paper, we develop SRN model of network virtualization based on virtual switch. Measures of interest such as switching delay and throughput are considered. These measures are expressed in terms of the expected values of reward rate functions for SRNs. Numerical results are obtained according to the virtual switch capacity and number of active VMs.

Distraction intermaxillaire chirurgicalement assisté dans le syndrome d’apnées hypopnées obstructives du sommeil (SAHOS)

We apply language theory to compare the expressive power of infinite-state models that extend Petri nets with features like coloured tokens and/or whole place operations. Specifically, we consider extensions of Petri nets in which tokens carry pure names dynamically generated with special ν-transitions (ν-PN) and compare their expressiveness with transfer and reset nets with black indistinguishable tokens (Affine Well-Structured Nets), and nets in which tokens carry data taken from a linearly ordered domain (Data nets and CMRS). All these models are well-structured transition systems. In order to compare these models we consider the families of languages they recognize, using coverability as the accepting condition. With this criterion, we prove that ν-PNs are in between AWNs and Data Nets/CMRS, but equivalent to an extension of ν-PN with whole-place operations. These results extend the currently known classification of the expressive power of well-structured transition systems. Finally, we study several problems regarding (coverability) languages of AWN and ν-PN.