About Dynamical Systems Appearing in the Microscopic Traffic Modeling

Motivated by microscopic traffic modeling, we analyze dynamical systems which have a piecewise linear concave dynamics not necessarily monotonic. We introduce a deterministic Petri net extension where edges may have negative weights. The dynamics of these Petri nets are well-defined and may be described by a generalized matrix with a submatrix in the standard algebra with possibly negative entries, and another submatrix in the minplus algebra. When the dynamics is additively homogeneous, a generalized additive eigenvalue may be introduced, and the ergodic theory may be used to define a growth rate under additional technical assumptions. In the traffic example of two roads with one junction, we compute explicitly the eigenvalue and we show, by numerical simulations, that these two quantities (the additive eigenvalue and the growth rate) are not equal, but are close to each other. With this result, we are able to extend the well-studied notion of fundamental traffic diagram (the average flow as a function of the car density on a road) to the case of two roads with one junction and give a very simple analytic approximation of this diagram where four phases appear with clear traffic interpretations. Simulations show that the fundamental diagram shape obtained is also valid for systems with many junctions. To simulate these systems, we have to compute their dynamics, which are not quite simple. For building them in a modular way, we introduce generalized parallel, series and feedback compositions of piecewise linear concave dynamics.Comment: PDF 38 page

Model Checking Markov Chains with Actions and State Labels

In the past, logics of several kinds have been proposed for reasoning about discrete- or continuous-time Markov chains. Most of these logics rely on either state labels (atomic propositions) or on transition labels (actions). However, in several applications it is useful to reason about both state-properties and action-sequences. For this purpose, we introduce the logic asCSL which provides powerful means to characterize execution paths of Markov chains with actions and state labels. asCSL can be regarded as an extension of the purely state-based logic asCSL (continuous stochastic logic). \ud In asCSL, path properties are characterized by regular expressions over actions and state-formulas. Thus, the truth value of path-formulas does not only depend on the available actions in a given time interval, but also on the validity of certain state formulas in intermediate states.\ud We compare the expressive power of CSL and asCSL and show that even the state-based fragment of asCSL is strictly more expressive than CSL if time intervals starting at zero are employed. Using an automaton-based technique, an asCSL formula and a Markov chain with actions and state labels are combined into a product Markov chain. For time intervals starting at zero we establish a reduction of the model checking problem for asCSL to CSL model checking on this product Markov chain. The usefulness of our approach is illustrated by through an elaborate model of a scalable cellular communication system for which several properties are formalized by means of asCSL-formulas, and checked using the new procedure

A bibliography on formal methods for system specification, design and validation

Literature on the specification, design, verification, testing, and evaluation of avionics systems was surveyed, providing 655 citations. Journal papers, conference papers, and technical reports are included. Manual and computer-based methods were employed. Keywords used in the online search are listed

Petri net modeling of cyber-physical attacks on smart grid

This paper investigates the use of Petri nets for modeling coordinated cyber-physical attacks on the smart grid. Petri nets offer more flexibility and expressiveness than traditional attack trees to represent the actions of simultaneous attackers. However, Petri net models for attacks on very large critical infrastructures such as the smart grid require a great amount of manual effort and detailed expertise in cyber-physical threats. To overcome these obstacles, we propose a novel hierarchical method to construct large Petri nets from a number of smaller Petri nets that can be created separately by different domain experts. The construction method is facilitated by a model description language that enables identical places in different Petri nets to be matched. The new modeling approach is described for an example attack on smart meters, and its efficacy is demonstrated by a proof-of-concept Python program

SIMULATION AND ANALYSIS OF PENTOSE PHOSPHATE PATHWAY IN PLASMODIUM FALCIPARUM USING COLORED PETRI NETS MODEL

Plasmodium falciparum is a protozoan parasite and the deadliest of five human malaria species which is responsible for the majority of malaria related deaths in humans. The erythrocytes’ stage of Plasmodium falciparum depend on Pentose Pathway as an alternative source of energy and it releases electrons used in protecting the Plasmodium falciparum from its host. Colored Petri Net has been recognized as one of the important models in modelling and analyzing biological pathways. It is an accurate qualitative and quantitative modelling tool for modeling complex biological systems. In this work, the modeling of the pentose phosphate pathway in Plasmodium falciparum is presented using the Petri Net Markup Language (PNML). The Colored Petri Net (CPN) models based on the Petri Net representation and the conservation and kinetic equations were used to examine the dynamic behavior of the metabolic pathway. The usefulness of Petri Nets is demonstrated for the quantitative analysis of the pathway. We obtained data from Biocyc database. The constructed model was viewed through the Colored Petri Net Tool (CPN tool 4.0). Specific drug targets called the essential reactions within the pathway were identified, listed and proposed. These essential reactions would alter the functioning of the pathway which would affect the energy and protection needs of the parasite therefore leading to the death of the parasite in the human red blood cell

Computing multi-scale organizations built through assembly

The ability to generate and control assembling structures built over many orders of magnitude is an unsolved challenge of engineering and science. Many of the presumed transformational benefits of nanotechnology and robotics are based directly on this capability. There are still significant theoretical difficulties associated with building such systems, though technology is rapidly ensuring that the tools needed are becoming available in chemical, electronic, and robotic domains. In this thesis a simulated, general-purpose computational prototype is developed which is capable of unlimited assembly and controlled by external input, as well as an additional prototype which, in structures, can emulate any other computing device. These devices are entirely finite-state and distributed in operation. Because of these properties and the unique ability to form unlimited size structures of unlimited computational power, the prototypes represent a novel and useful blueprint on which to base scalable assembly in other domains. A new assembling model of Computational Organization and Regulation over Assembly Levels (CORAL) is also introduced, providing the necessary framework for this investigation. The strict constraints of the CORAL model allow only an assembling unit of a single type, distributed control, and ensure that units cannot be reprogrammed - all reprogramming is done via assembly. Multiple units are instead structured into aggregate computational devices using a procedural or developmental approach. Well-defined comparison of computational power between levels of organization is ensured by the structure of the model. By eliminating ambiguity, the CORAL model provides a pragmatic answer to open questions regarding a framework for hierarchical organization. Finally, a comparison between the designed prototypes and units evolved using evolutionary algorithms is presented as a platform for further research into novel scalable assembly. Evolved units are capable of recursive pairing ability under the control of a signal, a primitive form of unlimited assembly, and do so via symmetry-breaking operations at each step. Heuristic evidence for a required minimal threshold of complexity is provided by the results, and challenges and limitations of the approach are identified for future evolutionary studies

Evaluating Resilience of Cyber-Physical-Social Systems

Nowadays, protecting the network is not the only security concern. Still, in cyber security, websites and servers are becoming more popular as targets due to the ease with which they can be accessed when compared to communication networks. Another threat in cyber physical social systems with human interactions is that they can be attacked and manipulated not only by technical hacking through networks, but also by manipulating people and stealing users’ credentials. Therefore, systems should be evaluated beyond cy- ber security, which means measuring their resilience as a piece of evidence that a system works properly under cyber-attacks or incidents. In that way, cyber resilience is increas- ingly discussed and described as the capacity of a system to maintain state awareness for detecting cyber-attacks. All the tasks for making a system resilient should proactively maintain a safe level of operational normalcy through rapid system reconfiguration to detect attacks that would impact system performance. In this work, we broadly studied a new paradigm of cyber physical social systems and defined a uniform definition of it. To overcome the complexity of evaluating cyber resilience, especially in these inhomo- geneous systems, we proposed a framework including applying Attack Tree refinements and Hierarchical Timed Coloured Petri Nets to model intruder and defender behaviors and evaluate the impact of each action on the behavior and performance of the system.Hoje em dia, proteger a rede não é a única preocupação de segurança. Ainda assim, na segurança cibernética, sites e servidores estão se tornando mais populares como alvos devido à facilidade com que podem ser acessados quando comparados às redes de comu- nicação. Outra ameaça em sistemas sociais ciberfisicos com interações humanas é que eles podem ser atacados e manipulados não apenas por hackers técnicos através de redes, mas também pela manipulação de pessoas e roubo de credenciais de utilizadores. Portanto, os sistemas devem ser avaliados para além da segurança cibernética, o que significa medir sua resiliência como uma evidência de que um sistema funciona adequadamente sob ataques ou incidentes cibernéticos. Dessa forma, a resiliência cibernética é cada vez mais discutida e descrita como a capacidade de um sistema manter a consciência do estado para detectar ataques cibernéticos. Todas as tarefas para tornar um sistema resiliente devem manter proativamente um nível seguro de normalidade operacional por meio da reconfi- guração rápida do sistema para detectar ataques que afetariam o desempenho do sistema. Neste trabalho, um novo paradigma de sistemas sociais ciberfisicos é amplamente estu- dado e uma definição uniforme é proposta. Para superar a complexidade de avaliar a resiliência cibernética, especialmente nesses sistemas não homogéneos, é proposta uma estrutura que inclui a aplicação de refinamentos de Árvores de Ataque e Redes de Petri Coloridas Temporizadas Hierárquicas para modelar comportamentos de invasores e de- fensores e avaliar o impacto de cada ação no comportamento e desempenho do sistema

Complete Specification of DDM Mechanisms

The specification of DDM (Distributed Decision-Making) algorithms is addressed. The modeling technique presented is based on well-known extensions to Petri-Nets (PNs). Transition-enabling functions with a domain corresponding to the marking of a net are used to express the semantics of decision-making. Furthermore, the algorithm structural characteristics of global state representation and topology are incorporated. Finally, the dynamic nature of evolution of system state, interaction with processes external to the computation, and the interprocess communication aspects of the mechanism are also modeled. The elements of analysis associated with this model are described, but not detailed in the scope of this paper