On detectability of labeled Petri nets and finite automata

Detectability is a basic property of dynamic systems: when it holds an observer can use the current and past values of the observed output signal produced by a system to reconstruct its current state. In this paper, we consider properties of this type in the framework of discrete-event systems modeled by labeled Petri nets and finite automata. We first study weak approximate detectability. This property implies that there exists an infinite observed output sequence of the system such that each prefix of the output sequence with length greater than a given value allows an observer to determine if the current state belongs to a given set. We prove that the problem of verifying this property is undecidable for labeled Petri nets, and PSPACE-complete for finite automata. We also consider one new concept called eventual strong detectability. The new property implies that for each possible infinite observed output sequence, there exists a value such that each prefix of the output sequence with length greater than that value allows reconstructing the current state. We prove that for labeled Petri nets, the problem of verifying eventual strong detectability is decidable and EXPSPACE-hard, where the decidability result holds under a mild promptness assumption. For finite automata, we give a polynomial-time verification algorithm for the property. In addition, we prove that strong detectability is strictly stronger than eventual strong detectability for labeled Petri nets and even for deterministic finite automata

Coinduction in control of partially observed discrete-event systems

Coalgebra and coinduction provide new results and insights for the supervisory control of discrete-event systems (DES) with partial observations. In the case of full observations, coinduction has been used to define a new operation on languages called supervised product, which represents the language of the closed-loop system. The first language acts as a supervisor and the second as an open-loop system (plant). We show first that the supervised product is equal to the infimal controllable superlanguage of the supervisor's (specification) language with respect to the plant language. This can be generalized to the partial observation case, where the supervised product is shown to be equal to the infimal controllable and observable superlanguage. There are two different control laws for partially observed DES, that give the same closed-loop system if the specification is observable: permissive and antipermissive. A variation on the supervised product is presented, which corresponds to the control policy with the issue of of observability separated from the issue of controllability. It is shown to be equal to the infimal observable superlanguage. Similar idea for the antipermissive control law leads to a maximal observable sublanguage that contains the supremal normal sublanguage. We present an algorithm for its computation

Coinduction in control of partially observed discrete-event systems

Coalgebra and coinduction provide new results and insights for the supervisory control of discrete-event systems (DES) with partial observations. In the case of full observations, coinduction has been used to define a new operation on languages called supervised product, which represents the language of the closed-loop system. The first language acts as a supervisor and the second as an open-loop system (plant). We show first that the supervised product is equal to the infimal controllable superlanguage of the supervisor's (specification) language with respect to the plant language. This can be generalized to the partial observation case, where the supervised product is shown to be equal to the infimal controllable and observable superlanguage. There are two different control laws for partially observed DES, that give the same closed-loop system if the specification is observable: permissive and antipermissive. A variation on the supervised product is presented, which corresponds to the control policy with the issue of of observability separated from the issue of controllability. It is shown to be equal to the infimal observable superlanguage. Similar idea for the antipermissive control law leads to a maximal observable sublanguage that contains the supremal normal sublanguage. We present an algorithm for its computation

Detectability Of Fuzzy Discrete Event Systems

Dynamic systems that can be modeled in terms of discrete states and a synchronous events are known as discrete event systems (DES). A DES is defined in terms of states, events, transition dynamics, and initial state. Knowing the system’s state is crucial in many applications for certain actions (events) to be taken. A DES system is considered a fuzzy discrete event system (FDES) if its states and events are vague in nature; for such systems, the system can be in more than one state at the same time with different degrees of possibility (membership). In this research we introduce a fuzzy discrete event system with constraints (FDESwC) and investigate its detectabilities. This research aims to address the gap in previous studies and extend existing definitions of detectability of DES to include the detectability in systems with substantial vagueness such as FDES. These definitions are first reformulated to introduce N-detectability for DES, which are further extended to define four main types of detectabilities for FDES: strong N-detectability, (weak) N-detectability, strong periodic N-detectability, and (weak) periodic N-detectability. We first partition the FDES into trajectories of a length dictated by the depth of the event’s string (length of the event sequence); each trajectory consists of a number of nodes, which are further investigated for detectability by examining them against the newly introduced certainty criterion. Matrix computation algorithms and fuzzy logic operations are adopted to calculate the state estimates based on the current state and the occurring events. Vehicle dynamics control example is used to demonstrate the practical aspect of developed theorems in real-world applications

Robot introspection through learned hidden Markov models

In this paper we describe a machine learning approach for acquiring a model of a robot behaviour from raw sensor data. We are interested in automating the acquisition of behavioural models to provide a robot with an introspective capability. We assume that the behaviour of a robot in achieving a task can be modelled as a finite stochastic state transition system. Beginning with data recorded by a robot in the execution of a task, we use unsupervised learning techniques to estimate a hidden Markov model (HMM) that can be used both for predicting and explaining the behaviour of the robot in subsequent executions of the task. We demonstrate that it is feasible to automate the entire process of learning a high quality HMM from the data recorded by the robot during execution of its task.The learned HMM can be used both for monitoring and controlling the behaviour of the robot. The ultimate purpose of our work is to learn models for the full set of tasks associated with a given problem domain, and to integrate these models with a generative task planner. We want to show that these models can be used successfully in controlling the execution of a plan. However, this paper does not develop the planning and control aspects of our work, focussing instead on the learning methodology and the evaluation of a learned model. The essential property of the models we seek to construct is that the most probable trajectory through a model, given the observations made by the robot, accurately diagnoses, or explains, the behaviour that the robot actually performed when making these observations. In the work reported here we consider a navigation task. We explain the learning process, the experimental setup and the structure of the resulting learned behavioural models. We then evaluate the extent to which explanations proposed by the learned models accord with a human observer's interpretation of the behaviour exhibited by the robot in its execution of the task

Minimization of Sensor Activation in Discrete-Event Systems with Control Delays and Observation Delays

In discrete-event systems, to save sensor resources, the agent continuously adjusts sensor activation decisions according to a sensor activation policy based on the changing observations. However, new challenges arise for sensor activations in networked discrete-event systems, where observation delays and control delays exist between the sensor systems and the agent. In this paper, a new framework for activating sensors in networked discrete-event systems is established. In this framework, we construct a communication automaton that explicitly expresses the interaction process between the agent and the sensor systems over the observation channel and the control channel. Based on the communication automaton, we can define dynamic observations of a communicated string. To guarantee that a sensor activation policy is physically implementable and insensitive to random control delays and observation delays, we further introduce the definition of delay feasibility. We show that a delay feasible sensor activation policy can be used to dynamically activate sensors even if control delays and observation delays exist. A set of algorithms are developed to minimize sensor activations in a transition-based domain while ensuring a given specification condition is satisfied. A practical example is provided to show the application of the developed sensor activation methods. Finally, we briefly discuss how to extend the proposed framework to a decentralized sensing architecture

Stochastic spatial modelling of DNA methylation patterns and moment-based parameter estimation

In the first part of this thesis, we introduce and analyze spatial stochastic models for DNA methylation, an epigenetic mark with an important role in development. The underlying mechanisms controlling methylation are only partly understood. Several mechanistic models of enzyme activities responsible for methylation have been proposed. Here, we extend existing hidden Markov models (HMMs) for DNA methylation by describing the occurrence of spatial methylation patterns with stochastic automata networks. We perform numerical analysis of the HMMs applied to (non-)hairpin bisulfite sequencing KO data and accurately predict the wild-type data from these results. We find evidence that the activities of Dnmt3a/b responsible for de novo methylation depend on the left but not on the right CpG neighbors. The second part focuses on parameter estimation in chemical reaction networks (CRNs). We propose a generalized method of moments (GMM) approach for inferring the parameters of CRNs based on a sophisticated matching of the statistical moments of the stochastic model and the sample moments of population snapshot data. The proposed parameter estimation method exploits recently developed moment-based approximations and provides estimators with desirable statistical properties when many samples are available. The GMM provides accurate and fast estimations of unknown parameters of CRNs. The accuracy increases and the variance decreases when higher-order moments are considered.Im ersten Teil der Arbeit führen wir eine Analyse für spatielle stochastische Modelle der DNA Methylierung, ein wichtiger epigenetischer Marker in der Entwicklung, durch. Die zugrunde liegenden Mechanismen der Methylierung werden noch nicht vollständig verstanden. Mechanistische Modelle beschreiben die Aktivität der Methylierungsenzyme. Wir erweitern bestehende Hidden Markov Models (HMMs) zur DNA Methylierung durch eine Stochastic Automata Networks Beschreibung von spatiellen Methylierungsmustern. Wir führen eine numerische Analyse der HMMs auf bisulfit-sequenzierten KO Datens¨atzen aus und nutzen die Resultate, um die Wildtyp-Daten erfolgreich vorherzusagen. Unsere Ergebnisse deuten an, dass die Aktivitäten von Dnmt3a/b, die überwiegend für die de novo Methylierung verantwortlich sind, nur vom Methylierungsstatus des linken, nicht aber vom rechten CpG Nachbarn abhängen. Der zweite Teil befasst sich mit Parameterschätzung in chemischen Reaktionsnetzwerken (CRNs). Wir führen eine Verallgemeinerte Momentenmethode (GMM) ein, die die statistischen Momente des stochastischen Modells an die Momente von Stichproben geschickt anpasst. Die GMM nutzt hier kürzlich entwickelte, momentenbasierte Näherungen, liefert Schätzer mit wünschenswerten statistischen Eigenschaften, wenn genügend Stichproben verfügbar sind, mit schnellen und genauen Schätzungen der unbekannten Parameter in CRNs. Momente höherer Ordnung steigern die Genauigkeit des Schätzers, während die Varianz sinkt

VERIFICATION AND APPLICATION OF DETECTABILITY BASED ON PETRI NETS

In many real-world systems, due to limitations of sensors or constraints of the environment, the system dynamics is usually not perfectly known. However, the state information of the system is usually crucial for the purpose of decision making. The state of the system needs to be determined in many applications. Due to its importance, the state estimation problem has received considerable attention in the discrete event system (DES) community. Recently, the state estimation problem has been studied systematically in the framework of detectability. The detectability properties characterize the possibility to determine the current and the subsequent states of a system after the observation of a finite number of events generated by the system. To model and analyze practical systems, powerful DES models are needed to describe the different observation behaviors of the system. Secondly, due to the state explosion problem, analysis methods that rely on exhaustively enumerating all possible states are not applicable for practical systems. It is necessary to develop more efficient and achievable verification methods for detectability. Furthermore, in this thesis, efficient detectability verification methods using Petri nets are investigated, then detectability is extended to a more general definition (C-detectability) that only requires that a given set of crucial states can be distinguished from other states. Formal definitions and efficient verification methods for C-detectability properties are proposed. Finally, C-detectability is applied to the railway signal system to verify the feasibility of this property: 1. Four types of detectability are extended from finite automata to labeled Petri nets. In particular, strong detectability, weak detectability, periodically strong detectability, and periodically weak detectability are formally defined in labeled Petri nets. 2. Based on the notion of basis reachability graph (BRG), a practically efficient approach (the BRG-observer method) to verify the four detectability properties in bounded labeled Petri nets is proposed. Using basis markings, there is no need to enumerate all the markings that are consistent with an observation. It has been shown by other researchers that the size of the BRG is usually much smaller than the size of the reachability graph (RG). Thus, the method improves the analysis efficiency and avoids the state space explosion problem. 3. Three novel approaches for the verification of the strong detectability and periodically strong detectability are proposed, which use three different structures whose construction has a polynomial complexity. Moreover, rather than computing all cycles of the structure at hand, which is NP-hard, it is shown that strong detectability can be verified looking at the strongly connected components whose computation also has a polynomial complexity. As a result, they have lower computational complexity than other methods in the literature. 4. Detectability could be too restrictive in real applications. Thus, detectability is extended to C-detectability that only requires that a given set of crucial states can be distinguished from other states. Four types of C-detectability are defined in the framework of labeled Petri nets. Moreover, efficient approaches are proposed to verify such properties in the case of bounded labeled Petri net systems based on the BRG. 5. Finally, a general modeling framework of railway systems is presented for the states estimation using labeled Petri nets. Then, C-detectability is applied to railway signal systems to verify its feasibility in the real-world system. Taking the RBC handover procedure in the Chinese train control system level 3 (CTCS-3) as an example, the RBC handover procedure is modeled using labeled Petri nets. Then based on the proposed approaches, it is shown that that the RBC handover procedure satisfies strongly C-detectability

Non-determinism in the narrative structure of video games

PhD ThesisAt the present time, computer games represent a finite interactive system. Even in their more experimental forms, the number of possible interactions between player and NPCs (non-player characters) and among NPCs and the game world has a finite number and is led by a deterministic system in which events can therefore be predicted. This implies that the story itself, seen as the series of events that will unfold during gameplay, is a closed system that can be predicted a priori. This study looks beyond this limitation, and identifies the elements needed for the emergence of a non-finite, emergent narrative structure. Two major contributions are offered through this research. The first contribution comes in the form of a clear categorization of the narrative structures embracing all video game production since the inception of the medium. In order to look for ways to generate a non-deterministic narrative in games, it is necessary to first gain a clear understanding of the current narrative structures implemented and how their impact on users’ experiencing of the story. While many studies have observed the storytelling aspect, no attempt has been made to systematically distinguish among the different ways designers decide how stories are told in games. The second contribution is guided by the following research question: Is it possible to incorporate non-determinism into the narrative structure of computer games? The hypothesis offered is that non-determinism can be incorporated by means of nonlinear dynamical systems in general and Cellular Automata in particular