Inclusion dynamics hybrid automata

Hybrid systems are dynamical systems with the ability to describe mixed discrete-continuous evolution of a wide range of systems. Consequently, at first glance, hybrid systems appear powerful but recalcitrant, neither yielding to analysis and reasoning through a purely continuous-time modeling as with systems of differential equations, nor open to inferential processes commonly used for discrete state-transition systems such as finite state automata. A convenient and popular model, called hybrid automata, was introduced to model them and has spurred much interest on its tractability as a tool for inference and model checking in a general setting. Intuitively, a hybrid automaton is simply a “finite-state” automaton with each state augmented by continuous variables, which evolve according to a set of well-defined continuous laws, each specified separately for each state. This article investigates both the notion of hybrid automaton and the model checking problem over such a structure. In particular, it relates first-order theories and analysis results on multivalued maps and reduces the bounded reachability problem for hybrid automata whose continuous laws are expressed by inclusions (x′f(x,t)) to a decidability problem for first-order formulæ over the reals. Furthermore, the paper introduces a class of hybrid automata for which the reachability problem can be decided and shows that the problem of deciding whether a hybrid automaton belongs to this class can be again decided using first-order formulæ over the reals. Despite the fact that the bisimulation quotient for this class of hybrid automata can be infinite, we show that our techniques permit effective model checking for a nontrivial fragment of CTL.     

Formal verification of SysML diagram using case studies of real-time system

System and software engineers use SysML models for the graphical modeling of the embedded systems. The SysML models are inadequate to express the discrete controllers with continuously evolving variables. The real-time constraints such as discrete and continuous dynamics are considered to be an important aspect in embedded systems. The lack of support of real-time aspect in SysML model can lead to inexplicit modeling of the embedded systems. The imprecise modeling could cause catastrophic results when an embedded system gets operational. In this paper, we propose hybrid automata-based semantics that supports the discrete and continuous behavior in upgraded SysML block diagram. The upgraded SysML block diagram is used for the modeling of the embedded system. Furthermore, we use model checker PRISM for the early design verification of upgraded SysML block diagram. Finally, we demonstrate the effectiveness of our proposed approach with the help of two case studies “temperature control system” and “water level control system”.

     

Hybrid MARTE statecharts

The specification of modeling and analysis of real-time and embedded systems (MARTE) is an extension of the unified modeling language (UML) in the domain of real-time and embedded systems. Even though MARTE time model offers a support to describe both discrete and dense clocks, the biggest effort has been put so far on the specification and analysis of discrete MARTE models. To address hybrid real-time and embedded systems, we propose to extend statecharts using both MARTE and the theory of hybrid automata. We call this extension hybrid MARTE statecharts. It provides an improvement over the hybrid automata in that: the logical time variables and the chronometric time variables are unified. The formal syntax and semantics of hybrid MARTE statecharts are given based on labeled transition systems and live transition systems. As a case study, we model the behavior of a train control system with hybrid MARTE statecharts to demonstrate the benefit.     

Hybrid automata, reachability, and Systems Biology

Hybrid automata are a powerful formalism for the representation of systems evolving according to both discrete and continuous laws. Unfortunately, undecidability soon emerges when one tries to automatically verify hybrid automata properties. An important verification problem is the reachability one that demands to decide whether a set of points is reachable from a starting region.If we focus on semi-algebraic hybrid automata the reachability problem is semi-decidable. However, high computational costs have to be afforded to solve it. We analyse this problem by exploiting some existing tools and we show that even simple examples cannot be efficiently solved. It is necessary to introduce approximations to reduce the number of variables, since this is the main source of runtime requirements. We propose some standard approximation methods based on Taylor polynomials and ad hoc strategies. We implement our methods within the software SAHA-Tool and we show their effectiveness on two biological examples: the Repressilator and the Delta-Notch protein signaling.     

Designer®—Intelligent expert system for intelligent manufacturing systems design

This survey on expert systems activities and trends in Yugoslavia offers some results already obtained in the domain of manufacturing science and technology. In the scope of a long-term research project “Intelligent Manufacturing Systems (IMS)—Theory and Application” a Designer® Intelligent Expert System for mafacturing engineering has been proposed and partially developed. Designer® IES is based on new developed knowledge automata theory enhanced with cellular automata concept. Induction learning by analogy and Quasimorphism knowledge mapping from real world to model world is used to generate a reasoning structure. The Intelligent Expert System is divided into three main subsystems, with a very large knowledge base:

• •Product designer
• •Process Designer, and
• •Production Planning and Control Designer.

All these segments were developed in pilot versions of expert systems for specific groups of activities inside each of these three domains.     

A universal planning system for hybrid domains

Many real world problems involve hybrid systems, subject to (continuous) physical effects and controlled by (discrete) digital equipments. Indeed, many efforts are being made to extend the current planning systems and modelling languages to support such kind of domains. However, hybrid systems often present also a nonlinear behaviour and planning with continuous nonlinear change that is still a challenging issue.     

The “book problem” and its neural correlates

Presence research can tell us why we feel present in the real world and can experience presence while using virtual reality technology (and movies and games) but has strikingly less to say on why we feel present in the scenes described in a book. Just how is it that the wonderful tangible detail of the real world or the complexity of digital technology can be matched and even surpassed by a story in a paperback book? This paper identifies a range of potential neurological solutions to this problem (and the “real world” and “dream” problems for good measure). We consider Jeannerod’s neural simulation of action, Grush’s emulation theory of representation and Rizzolatti’s work on mirror neurons as being candidate solutions to the “book problem”. We conclude by observing that these potential solutions further underline the “purpose” of presence is to act in the world whether it is real, virtual or solely in our imaginations.     

Syntax and consistent equation semantics of hybrid Chi

The hybrid χ (Chi) formalism integrates concepts from dynamics and control theory with concepts from computer science, in particular from process algebra and hybrid automata. It integrates ease of modeling with a straightforward, structured operational semantics. Its ‘consistent equation semantics’ enforces state changes to be consistent with delay predicates, that combine the invariant and flow clauses of hybrid automata. Ease of modeling is ensured by means of the following concepts: (1) different classes of variables: discrete and continuous, of subclass jumping or non-jumping, and algebraic; (2) strong time determinism of alternative composition in combination with delayable guards; (3) integration of urgent and non-urgent actions; (4) differential algebraic equations as a process term as in mathematics; (5) steady-state initialization; and 6) several user-friendly syntactic extensions. Furthermore, the χ formalism incorporates several concepts for complex system specification: (1) process terms for scoping that integrate abstraction, local variables, local channels and local recursion definitions; (2) process definition and instantiation that enable process re-use, encapsulation, hierarchical and/or modular composition of processes; and (3) different interaction mechanisms: handshake synchronization and synchronous communication that allow interaction between processes without sharing variables, and shared variables that enable modular composition of continuous-time or hybrid processes. The syntax and semantics are illustrated using several examples.     

On Hybrid Petri Nets

Petrinets (PNs) are widely used to model discrete event dynamic systems(computer systems, manufacturing systems, communication systems,etc). Continuous Petri nets (in which the markings are real numbersand the transition firings are continuous) were defined morerecently; such a PN may model a continuous system or approximatea discrete system. A hybrid Petri net can be obtained if onepart is discrete and another part is continuous. This paper isbasically a survey of the work of the authors' team on hybridPNs (definition, properties, modeling). In addition, it containsnew material such as the definition of extended hybrid PNs andseveral applications, explanations and comments about the timingsin Petri nets, more on the conflict resolution in hybrid PNs,and connection between hybrid PNs and hybrid automata. The paperis illustrated by many examples.     

Practical verification of decision-making in agent-based autonomous systems

We present a verification methodology for analysing the decision-making component in agent-based hybrid systems. Traditionally hybrid automata have been used to both implement and verify such systems, but hybrid automata based modelling, programming and verification techniques scale poorly as the complexity of discrete decision-making increases making them unattractive in situations where complex logical reasoning is required. In the programming of complex systems it has, therefore, become common to separate out logical decision-making into a separate, discrete, component. However, verification techniques have failed to keep pace with this development. We are exploring agent-based logical components and have developed a model checking technique for such components which can then be composed with a separate analysis of the continuous part of the hybrid system. Among other things this allows program model checkers to be used to verify the actual implementation of the decision-making in hybrid autonomous systems.     

Communication complexity and intrinsic universality in cellular automata

The notions of universality and completeness are central in the theories of computation and computational complexity. However, proving lower bounds and necessary conditions remains hard in most cases. In this article, we introduce necessary conditions for a cellular automaton to be “universal”, according to a precise notion of simulation, related both to the dynamics of cellular automata and to their computational power. This notion of simulation relies on simple operations of space–time rescaling and it is intrinsic to the model of cellular automata. Intrinsic universality, the derived notion, is stronger than Turing universality, but more uniform, and easier to define and study.Our approach builds upon the notion of communication complexity, which was primarily designed to study parallel programs, and thus is, as we show in this article, particulary well suited to the study of cellular automata: it allowed us to show, by studying natural problems on the dynamics of cellular automata, that several classes of cellular automata, as well as many natural (elementary) examples, were not intrinsically universal.     

Specification and synthesis of hybrid automata for physics-based animation

Physics-based animation programs can often be modeled in terms of hybrid automata. A hybrid automaton includes both discrete and continuous dynamical variables. The discrete variables define the automaton’s modes of behavior. The continuous variables are governed by mode-dependent differential equations. This paper describes a system for specifying and automatically synthesizing physics-based animation programs based on hybrid automata. The system presents a program developer with a family of parameterized specification schemata. Each schema describes a pattern of behavior as a hybrid automaton passes through a sequence of modes. The developer specifies a program by selecting one or more schemata and supplying application-specific instantiation parameters for each of them. Each schema is associated with a set of axioms in a logic of hybrid automata. The axioms serve to document the semantics of the specification schema. Each schema is also associated with a set of implementation rules. The rules synthesize program components implementing the specification in a general physics-based animation architecture. The system allows animation programs to be developed and tested in an incremental manner. The system itself can be extended to incorporate additional schemata for specifying new patterns of behavior, along with new sets of axioms and implementation rules. It has been implemented and tested on over a dozen examples. We believe this research is a significant step toward a specification and synthesis system that is flexible enough to handle a wide variety of animation programs, yet restricted enough to permit programs to be synthesized automatically.     

A FORMALIZATION OF SOME SIMULATION LANGUAGE CONCEPTS

A formalization of some simulation modeling concepts is described, which is used as a conceptual framework among simulationists and in the educational process. The notion of dynamic system is hierarchically constructed from attributes and classes: the domains of the classes are formed by elements with “similar” attributes and a set of classes is a system if it satisfies certain axioms. A simulation model is composed of two systems and four mappings also satisfying axioms. This conception reflects the capability of simulation languages to not only describe the dynamics of systems but also their structure. The theory is a framework for any sort of simulation models (discrete, continuous, combined, hybrid, analogue, galvanical, aerodynamical etc.) and allows a classification of the set of all simulation languages according to their semantics.     

Some applications of topology to program semantics

The relationship between programs and the set of partial correctness assertions that they satisfy, constitutes a Galois connection. The topology resulting from this Galois connection is closely related to the Lindenbaum baum topology for the language in which these partial correctness assertions are stated. This relationship provides us with a tool for understanding the incompleteness of Hoare Logics and for answering certain natural questions about the connection between the relational semantics and the partial correctness assertion semantics for programs, especially in connection with the question of modularity of programs. Two questions to which we shall find topological answers in this paper are “When is a language expressive for a program?”, and “When can we have rules of inference which are adequate to infer the properties of the complex program ±#β from those of its components ±,β?” We also obtain a natural answer to the question “What can the set{(A, B)|{A}±{B} is true) look like for arbitraryα?”.     

An extension of the inverse method to probabilistic timed automata

Probabilistic timed automata can be used to model systems in which probabilistic and timing behaviour coexist. Verification of probabilistic timed automata models is generally performed with regard to a single reference valuation π ₀ of the timing parameters. Given such a parameter valuation, we present a method for obtaining automatically a constraint K ₀ on timing parameters for which the reachability probabilities (1) remain invariant and (2) are equal to the reachability probabilities for the reference valuation. The method relies on parametric analysis of a non-probabilistic version of the probabilistic timed automata model using the “inverse method”. The method presents the following advantages. First, since K ₀ corresponds to a dense domain around π ₀ on which the system behaves uniformly, it gives us a measure of robustness of the system. Second, it allows us to obtain a valuation satisfying K ₀ which is as small as possible while preserving reachability probabilities, thus making the probabilistic analysis of the system easier and faster in practice. We provide examples of the application of our technique to models of randomized protocols, and introduce an extension of the method allowing the generation of a “probabilistic cartography” of a system.     

Approximate Comparison of Functions Computed by Distance Automata

Distance automata are automata weighted over the semiring \((\mathbb {N}\cup \{\infty \},\min , +)\) (the tropical semiring). Such automata compute functions from words to \(\mathbb {N}\cup \{\infty \}\). It is known from Krob that the problems of deciding ‘ f≤g’ or ‘ f=g’ for f and g computed by distance automata is an undecidable problem. The main contribution of this paper is to show that an approximation of this problem is decidable. We present an algorithm which, given ε>0 and two functions f,g computed by distance automata, answers “yes” if f≤(1?ε)g, “no” if f≦?g, and may answer “yes” or “no” in all other cases. The core argument behind this quasi-decision procedure is an algorithm which is able to provide an approximated finite presentation of the closure under products of sets of matrices over the tropical semiring. Lastly, our theorem of affine domination gives better bounds on the precision of known decision procedures for cost automata, when restricted to distance automata.     

Reversible client/server interactions

In the setting of session behaviours, we study an extension of the concept of compliance when a disciplined form of backtracking and of output skipping is present. After adding checkpoints to the syntax of session behaviours, we formalise the operational semantics via an LTS, and define natural notions of checkpoint compliance and sub-behaviour, which we prove to be both decidable. Then we extend the operational semantics with skips and we show the decidability of the obtained compliance.     

On First-Order Logic and CPDA Graphs

Higher-order pushdown automata (n-PDA) are abstract machines equipped with a nested ‘stack of stacks of stacks’. Collapsible pushdown automata (n-CPDA) extend these devices by adding ‘links’ to the stack and are equi-expressive for tree generation with simply typed λY terms. Whilst the configuration graphs of HOPDA are well understood, relatively little is known about the CPDA graphs. The order-2 CPDA graphs already have undecidable MSO theories but it was only recently shown by Kartzow (Log. Methods Comput. Sci. 9(1), 2013) that first-order logic is decidable at the second level. In this paper we show the surprising result that first-order logic ceases to be decidable at order-3 and above. We delimit the fragments of the decision problem to which our undecidability result applies in terms of quantifer alternation and the orders of CPDA links used. Additionally we exhibit a natural sub-hierarchy enjoying limited decidability.     

A uniform approach to three-valued semantics for <Emphasis Type="Italic">μ</Emphasis>-calculus on abstractions of hybrid automata

In this paper, we consider the definition of a three-valued semantics for a μ-calculus on abstractions of hybrid automata. To this end, we first develop a framework that is general in the sense that it provides a preservation result for several possible semantics of the modal operators. In a second step, we instantiate our framework to two particular abstractions. To this end, a key issue is the consideration of both over- and underapproximated reachability, while classic simulation-based abstractions rely only on overapproximations, and therefore limit the preservation to the universal (μ-calculus’) fragment. To specialize our general result, we consider (1) modal abstractions, where the notions of ‘may’ and ‘must’ transitions are extended from the purely discrete to the hybrid time framework, and (2) so-called discrete bounded bisimulation abstractions.     

Results and perspectives on fault tolerant control for a class of hybrid systems

This article addresses the fault tolerant control (FTC) issue for a class of hybrid systems (HS) modelled by hybrid automata. Two kinds of faults are considered: continuous fault that affects each continuous system mode; discrete fault that affects the switching conditions. In these two faulty cases, the FTC design has two main objectives: (1) maintain the continuous performances including various stabilities of the origin and the output tracking/regulation behaviours along the trajectories of HS; (2) maintain the discrete specifications that have to be followed by HS, e.g. a desired switching sequence. The following three FTC methodologies are considered: FTC for HS with continuous stability goal; FTC for HS with discrete specifications; supervisory FTC design via hybrid control techniques. Some perspectives are also provided. This article provides the readers a survey on the main techniques that can be used to achieve these FTC goals of HS.