Language-measure-theoretic optimal control of probabilistic finite-state systems

Supervisory control theory for discrete event systems, introduced by Ramadge and Wonham, is based on a non-probabilistic formal language framework. However, models for physical processes inherently involve modelling errors and noise-corrupted observations, implying that any practical finite-state approximation would require consideration of event occurrence probabilities. Building on the concept of signed real measure of regular languages, this paper formulates a comprehensive theory for optimal control of finite-state probabilistic processes. It is shown that the resulting discrete-event supervisor is optimal in the sense of elementwise maximizing the renormalized langauge measure vector for the controlled plant behaviour and is efficiently computable. The theoretical results are validated through several examples including the simulation of an engineering problem.     

A fully abstract semantics of classes for Object-Z

This paper presents a fully abstract semantics of classes for the object oriented formal specification language Object-Z. Such a semantics includes no unnecessary syntactic details and, hence, describes a class in terms of the external behaviour of its objects only. The semantics, based on an extension of existing process models, defines a notion of behavioural equivalence which is stronger than that of CSP and weaker than that of CCS.     

A semantic equivalence for Bio-PEPA based on discretisation of continuous values

Bio-PEPA is a process algebra for modelling biological systems. An important aspect of Bio-PEPA is the ability it provides to discretise concentrations resulting in a smaller, more manageable state space. The discretisation is based on a step size which determines the size of each discrete level and also the number of levels. This paper considers the relationship between two discretisations of the same Bio-PEPA model that differ only in the step size and hence the number of levels, by using the idea of equivalence from concurrency and process algebra. We present a novel behavioural semantic equivalence, compression bisimilarity, and investigate when this equates two discretisations of the same model and the circumstances in which this equivalence is a congruence with respect to the synchronisation operator.     

SYSTEM THEORETIC FORMALISMS FOR COMBINED DISCRETE-CONTINUOUS SYSTEM SIMULATION

In this paper we present an approach to combined discrete-continuous modelling which can be used to model and simulate an intelligent multi-layer control architecture as can be found in high autonomy systems. The modelling approach is based on system theoretical concepts; the three system specification formalisms-differential equation, discrete time, and the discrete event system specification formalism-have been combined to facilitate multi-formalisms modelling. Simulation concepts are based on the abstract simulator concept for discrete event simulation developed by Zeigler. Similar simulation methods have been developed to simulate modular, hierarchical discrete time and differential equation specified systems as well as multi-formalism models. Included in the paper are several examples of multi-formalism models together with the simulation results from the STIMS environment-an implementation of the modelling and simulation concepts in Interlisp-D/LOOPS.     

A monotone framework for CCS

The calculus of communicating systems, CCS, was introduced by Robin Milner as a calculus for modelling concurrent systems. Subsequently several techniques have been developed for analysing such models in order to get further insight into their dynamic behaviour.In this paper we present a static analysis for approximating the control structure embedded within the models. We formulate the analysis as an instance of a monotone framework and thus draw on techniques that often are associated with the efficient implementation of classical imperative programming languages.We show how to construct a finite automaton that faithfully captures the control structure of a CCS model. Each state in the automaton records a multiset of the enabled actions and appropriate transfer functions are developed for transforming one state into another. A classical worklist algorithm governs the overall construction of the automaton and its termination is ensured using techniques from abstract interpretation.     

Modelling automated manufacturing systems using a modification of coloured petri nets

Automated manufacturing systems (AMS) are a class of systems exhibiting concurrency, asynchronicity and distributedness, and can be modelled using Petri nets. The advantage of using Petri nets is that they provide graphical models, with formal methods of analysis. However, graphical representation of Petri net models becomes difficult even for medium-sized systems since such graphs tend to become inconveniently large. Coloured Petri nets (CPN) are a variant which enables a more concise representation with the same modelling power. This paper develops a model for simulation of AMS whose correctness can be formally established, and which can be graphically represented and visually understood. It presents a modelling approach for AMS, based on a modified version of CPN, with enhanced modelling power. The proposed modifications result in highly compact graphical representations, and also render the model dynamic, i.e. capable of changing dynamically to reflect currently selected system parameters. These features make the proposed model ideally suited for discrete event simulation.     

Coloured Petri Nets and CPN Tools for modelling and validation of concurrent systems

Coloured Petri Nets (CPNs) is a language for the modelling and validation of systems in which concurrency, communication, and synchronisation play a major role. Coloured Petri Nets is a discrete-event modelling language combining Petri nets with the functional programming language Standard ML. Petri nets provide the foundation of the graphical notation and the basic primitives for modelling concurrency, communication, and synchronisation. Standard ML provides the primitives for the definition of data types, describing data manipulation, and for creating compact and parameterisable models. A CPN model of a system is an executable model representing the states of the system and the events (transitions) that can cause the system to change state. The CPN language makes it possible to organise a model as a set of modules, and it includes a time concept for representing the time taken to execute events in the modelled system. CPN Tools is an industrial-strength computer tool for constructing and analysing CPN models. Using CPN Tools, it is possible to investigate the behaviour of the modelled system using simulation, to verify properties by means of state space methods and model checking, and to conduct simulation-based performance analysis. User interaction with CPN Tools is based on direct manipulation of the graphical representation of the CPN model using interaction techniques, such as tool palettes and marking menus. A license for CPN Tools can be obtained free of charge, also for commercial use.     

Implementing Coloured Petri Nets Using a Functional Programming Language

Coloured Petri Nets (CPNs) are a graphically oriented modelling language for concurrent systems based on Petri Nets and the functional programming language Standard ML. Petri Nets provide the primitives for modelling concurrency and synchronisation. Standard ML provides the primitives for modelling data manipulation and for creating compact and parameterisable CPN models.Functional programming and Standard ML have played a major role in the development of CPNs and the CPN computer tools supporting modelling, simulation, verification, and performance analysis of concurrent systems. At the modelling language level, Standard ML has extended Petri Nets with the practical expressiveness required for modelling systems of the size and complexity found in typical industrial projects. At the implementation level, Standard ML has been used to implement the formal semantics of CPNs that provide the theoretical foundation of the CPN computer tools.This paper provides an overview of how functional programming and Standard ML are applied in the CPN modelling language and the supporting computer tools. We give a detailed presentation of the key algorithms and techniques used for implementing the formal semantics of CPNs, and we survey a number of case studies where CPNs have been used for the design and analysis of systems. We also demonstrate how the use of a Standard ML programming environment has allowed Petri Nets to be used for the implementation of systems.     

Robust supervisory control of timed discrete event systems under partial observation based on eligible time bounds: The existence conditions

This paper addresses a supervisory control problem for uncertain timed discrete event systems (DESs) under partial observation. An uncertain timed DES to be controlled is represented by a set of possible timed models based on the framework of Brandin and Wonham [(1994). Supervisory control of timed discrete event systems. IEEE Transactions on Automatic Control, 39(2), 329-342]. To avoid the state space explosion problem caused by tick events in the timed models, a notion of eligible time bounds is proposed for a single timed model obtained from the set of all possible timed models. Based on this notion, we present the necessary and sufficient conditions for the existence of a robust supervisor achieving a given language specification for the single timed model. Moreover, we show that the robust supervisor can also achieve the specification for any timed model in the set.     

Perceived consistency between process models

Process-aware information systems typically involve various kinds of process stakeholders. That, in turn, leads to multiple process models that capture a common process from different perspectives and at different levels of abstraction. In order to guarantee a certain degree of uniformity, the consistency of such related process models is evaluated using formal criteria. However, it is unclear how modelling experts assess the consistency between process models, and which kind of notion they perceive to be appropriate.In this paper, we focus on control flow aspects and investigate the adequacy of consistency notions. In particular, we report findings from an online experiment, which allows us to compare in how far trace equivalence and two notions based on behavioural profiles approximate expert perceptions on consistency. Analysing 69 expert statements from process analysts, we conclude that trace equivalence is not suited to be applied as a consistency notion, whereas the notions based on behavioural profiles approximate the perceived consistency of our subjects significantly. Therefore, our contribution is an empirically founded answer to the correlation of behaviour consistency notions and the consistency perception by experts in the field of business process modelling.     

Tile Formats for Located and Mobile Systems

Standard SOS formats are limited in their ability to define the operational semantics of process calculi with concurrency, causality, and mobility, and with bound names and name generation mechanisms. In this paper we describe a general approach, based on the tile model, to the definition of the operational semantics of process calculi. By providing tile systems for located CCS and asynchronous π-calculus we demonstrate that the proposed approach is more suited than SOS to provide a uniform treatment of concurrency and mobility within a compositional framework.     

Simulation of Generalised Semi-Markov Processes based on Graph Transformation Systems

Stochastic Graph Transformation combines graphical modelling of various software artefacts with stochastic analysis techniques. Existing approaches are restricted to processes with exponential time distribution. Such processes are sufficient for modelling a significant class of stochastic systems, however there are interesting systems which cannot be specified appropriately in such a framework. In several cases one needs to consider non-exponential time distributions. This paper proposes a stochastic model based on graph transformation with general probability distributions. This model is well suited to represent concurrency and performance aspects of architecture reconfiguration. It is also possible to apply Monte Carlo simulation techniques in order to analyse behaviour of complex stochastic systems. The new model is implemented and used to simulate simple networks.     

Transformation of GRAFCET to PLC code including hierarchical structures

GRAFCET is an advantageous modelling language for the specification of controllers in discrete event systems. It allows for hierarchically structuring a control program's specification based on the elements enclosing steps, partial-Grafcets and forcing orders. A method is already available for the automatic transformation of Grafcets¹ into PLC code but this method cannot keep the hierarchical structures due to limitations of the PLC language SFC. In this contribution a systematic approach to automatically transform Grafcets into PLC code while retaining the hierarchical structures is described.     

A framework to visualize equivalences between computational models of regular languages

We discuss how to increase and simplify the understanding of the equivalence relations between machine models and/or language representations of formal languages by means of the animation tool SAGEMoLiC. Our new educational tool permits the simulation of the execution of models of computation, as many other animation systems do, but its philosophy goes further than these of the usual systems since it allows for a true visualization of the key notions involved in the formal proofs of these equivalences. In contrast with the proposal of previous systems, our approach to visualize equivalence theorems is not a simple “step by step animation” of specific conversion algorithms between computational models and/or grammatical representations of formal languages, because we make emphasis on the key theoretical notions involved in the formal proofs of these equivalences.     

Agent-Based Simulation of Animal Behaviour

In the biological literature on animal behaviour, in addition to real experiments and field studies, also simulation experiments are a useful source of progress. Often specific mathematical modelling techniques are adopted and directly implemented in a programming language. Modelling more complex agent behaviours is less adequate using the usually adopted mathematical modelling techniques. The literature on AI and Agent Technology offers more specific methods to design and implement (also more complex) intelligent agents and agent societies on a conceptual level. One of these methods is the compositional multi-agent system design method DESIRE. In this paper it is shown how (depending on the complexity of the required behaviour) a simulation model for animal behaviour can be designed at a conceptual level in an agent-based manner. Different models are shown for different types of behaviour, varying from purely reactive behaviour to pro-active, social and adaptive behaviour. The compositional design method for multi-agent systems DESIRE and its software environment supports the conceptual and detailed design, and execution of these models. A number of experiments reported in the literature on animal behaviour have been simulated for different agent models.     

HYPE: Hybrid modelling by composition of flows

Hybrid systems are manifest in both the natural and the engineered world, and their complex nature, mixing discrete control and continuous evolution, make it difficult to predict their behaviour. In recent years several process algebras for modelling hybrid systems have appeared in the literature, aimed at addressing this problem. These all assume that continuous variables in the system are modelled monolithically, often with differential equations embedded explicitly in the syntax of the process algebra expression. In HYPE an alternative approach is taken which offers finer-grained modelling with each flow or influence affecting a variable modelled separately. The overall behaviour then emerges as the composition of flows. In this paper we give a detailed account of the HYPE process algebra, its semantics, and its use for verification of systems. We establish both syntactic conditions (well-definedness) and operational restrictions (well-behavedness) to ensure reasonable behaviour in HYPE models. Furthermore we consider how the equivalence relation defined for HYPE relates to other relations previously proposed in the literature, demonstrating that our fine-grained approach leads to a more discriminating notion of equivalence. We present the HYPE model of a standard hybrid system example, both establishing that our approach can reproduce the previously obtained results and demonstrating how our compositional approach supports variations of the problem in a straightforward and flexible way.     

Diagnosability of delay-deadline failures in fair real time discrete event models

In this article a method for failure diagnosis of real time discrete event systems (RTDES) with ‘fairness of traces’ has been developed. Discrete event system (DES) modelling framework with provision for associating timing information with the transitions are required for handling real time systems. RTDES models and timed DES (TDES) models are examples of such modelling frameworks. Failure diagnosis in untimed DES models enables only the study of diagnosability of failures resulting in a change in the logical behaviour of the failed system. In addition to logical failures, failure diagnosis in RTDES and TDES models also enables diagnosability of failures that change the timing behaviour of the system but maintain the logical behaviour. Many systems exhibit fairness of traces with respect to transitions in the sense that any trace that visits a state infinitely often has infinitely many occurrences of all the transitions that emanate from that state. The abstraction employed in obtaining their (timed) DES models often obliterates this property. The RTDES and TDES diagnosability conditions, proposed in the literature and which do not consider fairness, are shown to be inadequate in this article. A new diagnosability condition is achieved by taking into account this fairness property in the RTDES models and shown to be necessary and sufficient for such systems. An analysis of time complexity for analysing the diagnosability of systems with fairness of traces is presented.     

A general framework for concurrent simulation on neural networkmodels

The analysis of complex neural network models via analytical techniques is often quite difficult due to the large numbers of components involved and the nonlinearities associated with these components. The authors present a framework for simulating neural networks as discrete event nonlinear dynamical systems. This includes neural network models whose components are described by continuous-time differential equations or by discrete-time difference equations. Specifically, the authors consider the design and construction of a concurrent object-oriented discrete event simulation environment for neural networks. The use of an object-oriented language provides the data abstraction facilities necessary to support modification and extension of the simulation system at a high level of abstraction. Furthermore, the ability to specify concurrent processing supports execution on parallel architectures. The use of this system is demonstrated by simulating a specific neural network model on a general-purpose parallel computer     

Type theory and concurrency

This paper describes the use of an automated reasoning tool, the Nuprl system, to formalize Milner's Calculus of Communicating Systems (CCS). The goals of this work are two-fold: the first is to investigate the feasibility of using systems like Nuprl to handle the formal detail arising from reasoning about concurrency, while the second is to develop a framework in which various formalisms for reasoning about concurrency may be presented in an automated fashion. To these ends, an implementation in Nuprl of a formal theory of concurrency is described, an implementation of CCS in this mechanized semantic theory presented, and two means of analyzing CCS terms are investigated.     

Predictive analytics using statistical,learning, and ensemble methods to support real-time exploration of discrete event simulations

Discrete event simulations (DES) provide a powerful means for modeling complex systems and analyzing their behavior. DES capture all possible interactions between the entities they manage, which makes them highly expressive but also compute-intensive. These computational requirements often impose limitations on the breadth and/or depth of research that can be conducted with a discrete event simulation.This work describes our approach for leveraging the vast quantity of computing and storage resources available in both private organizations and public clouds to enable real-time exploration of discrete event simulations. Rather than directly targeting simulation execution speeds, we autonomously generate and execute novel scenario variants to explore a representative subset of the simulation parameter space. The corresponding outputs from this process are analyzed and used by our framework to produce models that accurately forecast simulation outcomes in real time, providing interactive feedback and facilitating exploratory research.Our framework distributes the workloads associated with generating and executing scenario variants across a range of commodity hardware, including public and private cloud resources. Once the models have been created, we evaluate their performance and improve prediction accuracy by employing dimensionality reduction techniques and ensemble methods. To make these models highly accessible, we provide a user-friendly interface that allows modelers and epidemiologists to modify simulation parameters and see projected outcomes in real time.