State Space Of Model Research Articles

Program verification using symbolic game semantics

We introduce a new symbolic representation of algorithmic game semantics, and show how it can be applied for efficient verification of open (incomplete) programs. The focus is on an Algol-like programming language which contains the core ingredients of imperative and functional languages, especially on its second-order recursion-free fragment with infinite data types. We revisit the regular-language representation of game semantics of this language fragment. By using symbolic values instead of concrete ones, we generalize the standard notions of regular-language and automata representations of game semantics to those of corresponding symbolic representations. In this way programs with infinite data types, such as integers, can be expressed as finite-state symbolic-automata although the standard automata representation is infinite-state, i.e. the standard regular-language representation has infinite summations. Moreover, in this way significant reductions of the state space of game semantics models are obtained. This enables efficient verification of programs by our prototype tool based on symbolic game models, which is illustrated with several examples.

A Hidden Markov Model based transitional description of camera networks

We consider the problem of building a transitional model of an initially uncalibrated camera network. More specifically, we discuss a Hidden Markov Model (HMM) based strategy in which the model's state-space is defined in terms of a partition of the physical network coverage. Transitions between any two such states are described by the distribution of the underlying Markov Process. Extending previous work in (Cenedese et al., 2010), we show how it is possible to infer the model structure and parameters from coordinate free observations and we introduce a novel performance index for model validation. We moreover show the predictive power of this HMM approach in simulated and real settings that comprise Pan-Tilt-Zoom (PTZ) cameras.

Dynamic Request Routing for Online Video-on-Demand Service: A Markov Decision Process Approach

We investigate the request routing problem in the CDN-based Video-on-Demand system. We model the system as a controlled queueing system including a dispatcher and several edge servers. The system is formulated as a Markov decision process (MDP). Since the MDP formulation suffers from the so-called “the curse of dimensionality” problem, we then develop a greedy heuristic algorithm, which is simple and can be implemented online, to approximately solve the MDP model. However, we do not know how far it deviates from the optimal solution. To address this problem, we further aggregate the state space of the original MDP model and use the bounded-parameter MDP (BMDP) to reformulate the system. This allows us to obtain a suboptimal solution with a known performance bound. The effectiveness of two approaches is evaluated in a simulation study.

Finite Abstractions of Max-Plus-Linear Systems

This work puts forward a novel technique to generate finite abstractions of autonomous and nonautonomous Max-Plus-Linear (MPL) models, a class of discrete-event systems used to characterize the dynamics of the timing related to successive events that synchronize autonomously. Nonautonomous versions of MPL models embed within their dynamics nondeterminism, namely a signal choice that is usually regarded as an exogenous control or schedule. In this paper, abstractions of MPL models are characterized as finite-state Labeled Transition Systems (LTS). LTS are obtained first by partitioning the state space (and, for the nonautonomous model, by covering the input space) of the MPL model and by associating states of the LTS to the introduced partitions, then by defining relations among the states of the LTS based on dynamical transitions between the corresponding partitions of the MPL state space, and finally by labeling the LTS edges according to the one-step timing properties of the events of the original MPL model. In order to establish formal equivalences, the finite abstractions are proven to either simulate or to bisimulate the original MPL model. This approach enables the study of general properties of the original MPL model by verifying (via model checking) equivalent logical specifications over the finite LTS abstraction. The computational aspects related to the abstraction procedure are thoroughly discussed and its performance is tested on a numerical benchmark.

On Gapped Phases with a Continuous Symmetry and Boundary Operators

We discuss the role of compact symmetry groups, G, in the classification of gapped ground state phases of quantum spin systems. We consider two representations of G on infinite subsystems. First, in arbitrary dimensions, we show that the ground state spaces of models within the same G-symmetric phase carry equivalent representations of the group for each finite or infinite sublattice on which they can be defined and on which they remain gapped. This includes infinite systems with boundaries or with non-trivial topologies. Second, for two classes of one-dimensional models, by two different methods, for G=SU(2) in one, and G⊂SU(d), in the other we construct explicitly an ‘excess spin’ operator that implements rotations of half of the infinite chain on the GNS Hilbert space of the ground state of the full chain. Since this operator is constructed as the limit of a sequence of observables, the representation itself is, in principle, experimentally observable. We claim that the corresponding unitary representation of G is closely related to the representation found at the boundary of half-infinite chains. We conclude with determining the precise relation between the two representations for the class of frustration-free models with matrix product ground states.

Particle filter‐based data assimilation for a three‐dimensional biological ocean model and satellite observations

We assimilate satellite observations of surface chlorophyll into a three‐dimensional biological ocean model in order to improve its state estimates using a particle filter referred to as sequential importance resampling (SIR). Particle Filters represent an alternative to other, more commonly used ensemble‐based state estimation techniques like the ensemble Kalman filter (EnKF). Unlike the EnKF, Particle Filters do not require normality assumptions about the model error structure and are thus suitable for highly nonlinear applications. However, their application in oceanographic contexts is typically hampered by the high dimensionality of the model's state space. We apply SIR to a high‐dimensional model with a small ensemble size (20) and modify the standard SIR procedure to avoid complications posed by the high dimensionality of the model state. Two extensions to the SIR include a simple smoother to deal with outliers in the observations, and state‐augmentation which provides the SIR with parameter memory. Our goal is to test the feasibility of biological state estimation with SIR for realistic models. For this purpose we compare the SIR results to a model simulation with optimal parameters with respect to the same set of observations. By running replicates of our main experiments, we assess the robustness of our SIR implementation. We show that SIR is suitable for satellite data assimilation into biological models and that both extensions, the smoother and state‐augmentation, are required for robust results and improved fit to the observations.

AFChecker: Effective model checking for context-aware adaptive applications

Context-aware adaptive applications continually sense and adapt to their changing environments. A large body of such applications relies on user-configured adaptation rules to customize their behavior. We call them rule-based context-aware applications (or RBAs for short). Due to the complexity required for adequately modeling environmental dynamics, adaptation faults are common in these RBAs. One promising approach to detecting such faults is to build a state transition model for an RBA, and exhaustively explore the model's state space. However, it can suffer from numerous false positives. For example, 78.6% of 784 reported faults for one popular RBA – PhoneAdapter, turn out to be false in a real deployment. In this paper, we address this false positive problem by inferring a domain model and an environment model for an RBA. The two models capture the hidden features inside user-configured adaptation rules as well as the RBA's running environment. We formulate these features as deterministic constraints and probabilistic constraints to prune false positives and effectively prioritize remaining faults. Our experiments on two real RBAs report that this approach successfully removes 46.5% of false positives and ranks 86.2% of true positives to the top of the fault list.

Complete synchronization of chaotic atmospheric models by connecting only a subset of state space

Abstract. Connected chaotic systems can, under some circumstances, synchronize their states with an exchange of matter and energy between the systems. This is the case for toy models like the Lorenz 63, and more complex models. In this study we perform synchronization experiments with two connected quasi-geostrophic (QG) models of the atmosphere with 1449 degrees of freedom. The purpose is to determine whether connecting only a subset of the model state space can still lead to complete synchronization (CS). In addition, we evaluated whether empirical orthogonal functions (EOF) form efficient basis functions for synchronization in order to limit the number of connections. In this paper, we show that only the intermediate spectral wavenumbers (5–12) need to be connected in order to achieve CS. In addition, the minimum connection timescale needed for CS is 7.3 days. Both the connection subset and the connection timescale, or strength, are consistent with the time and spatial scales of the baroclinic instabilities in the model. This is in line with the fact that the baroclinic instabilities are the largest source of divergence between the two connected models. Using the Lorenz 63 model, we show that EOFs are nearly optimal basis functions for synchronization. The QG model results show that the minimum number of EOFs that need to be connected for CS is a factor of three smaller than when connecting the original state variables.

Symbolic Representation of Algorithmic Game Semantics

In this paper we revisit the regular-language representation of game semantics of second-order recursion free Idealized Algol with infinite data types. By using symbolic values instead of concrete ones we generalize the standard notion of regular-language and automata representations to that of corresponding symbolic representations. In this way terms with infinite data types, such as integers, can be expressed as finite symbolic-automata although the standard automata interpretation is infinite. Moreover, significant reductions of the state space of game semantics models are obtained. This enables efficient verification of terms, which is illustrated with several examples.

Petri Nets based Production System Model Simplification

Petri nets own graphical description ability based on solid mathematical foundation, this makes it a possible tool for analyzing complex system such as manufacturing system, but using Petri nets directly in large scale system will lead to state explosion. A Generalized Stochastic Petri Nets model of a repairable manufacturing cell is setup. As the first step to solve system state explosion problem, this 4 transitions model is transformed into a model with only one transition. Serial processing systems and parallel systems composed by such cells are transformed on the basis of cell model transformation, and such transformations are compared with those in other researches. The method presented in this paper helps to simplify system model and decrease system state space, and thus makes it feasible to use Petri nets in complex systems. Ill. 8, bibl. 12 (in English; abstracts in English and Lithuanian).DOI: http://dx.doi.org/10.5755/j01.eee.123.7.2388

Complete dynamic modeling and approximate state space equations of the flexible link manipulator

This work treats the problem of dynamic modeling and state space approximation for robotic manipulators with flexibility. Case studies are planar manipulators with a single flexible link together with clamped-free ends and tip mass conditions. In this paper, complete dynamic modeling of the flexible beam without premature linearization in the formulation of the dynamics equations is developed, whereby this model is capable of reproducing nonlinear dynamic effects, such as the beam stiffening due to the centrifugal and the Coriolis forces induced by rotation of the joints, giving it the capability to predict reliable dynamic behavior. On the other hand, in order to show the joint flexibility effects on the model dynamic behaviors, manipulator with structural and joint flexibility is considered. Thus, a reliable model for flexible beam is then presented. The model is founded on two basic assumptions: inextensibility of the neutral fiber and moderate rotations of the cross sections in order to account for the foreshortening of the beam due to bending. To achieve flexible manipulator control, the standard form of state space equations for a flexible manipulator system (flexible link and actuator) is very important. In this study, finite difference method for discretization of the dynamic equations is used and the state space equations of the flexible link with tip mass considering complete dynamic of the system are obtained. Simulation results indicated substantial improvements on dynamic behavior and it is shown that the joint flexibility has a considerable effect on the dynamic behavior of rotating flexible arm that should not be simply neglected. The effects of tip mass is proved to be increasing the elastic deformations’ amplitudes and increasing stability.

A Simplified Baseband Prefilter Model with Adaptive Kalman Filter for Ultra-Tight COMPASS/INS Integration

COMPASS is an indigenously developed Chinese global navigation satellite system and will share many features in common with GPS (Global Positioning System). Since the ultra-tight GPS/INS (Inertial Navigation System) integration shows its advantage over independent GPS receivers in many scenarios, the federated ultra-tight COMPASS/INS integration has been investigated in this paper, particularly, by proposing a simplified prefilter model. Compared with a traditional prefilter model, the state space of this simplified system contains only carrier phase, carrier frequency and carrier frequency rate tracking errors. A two-quadrant arctangent discriminator output is used as a measurement. Since the code tracking error related parameters were excluded from the state space of traditional prefilter models, the code/carrier divergence would destroy the carrier tracking process, and therefore an adaptive Kalman filter algorithm tuning process noise covariance matrix based on state correction sequence was incorporated to compensate for the divergence. The federated ultra-tight COMPASS/INS integration was implemented with a hardware COMPASS intermediate frequency (IF), and INS's accelerometers and gyroscopes signal sampling system. Field and simulation test results showed almost similar tracking and navigation performances for both the traditional prefilter model and the proposed system; however, the latter largely decreased the computational load.

Dynamical estimation of neuron and network properties II: path integral Monte Carlo methods

Hodgkin-Huxley (HH) models of neuronal membrane dynamics consist of a set of nonlinear differential equations that describe the time-varying conductance of various ion channels. Using observations of voltage alone we show how to estimate the unknown parameters and unobserved state variables of an HH model in the expected circumstance that the measurements are noisy, the model has errors, and the state of the neuron is not known when observations commence. The joint probability distribution of the observed membrane voltage and the unobserved state variables and parameters of these models is a path integral through the model state space. The solution to this integral allows estimation of the parameters and thus a characterization of many biological properties of interest, including channel complement and density, that give rise to a neuron's electrophysiological behavior. This paper describes a method for directly evaluating the path integral using a Monte Carlo numerical approach. This provides estimates not only of the expected values of model parameters but also of their posterior uncertainty. Using test data simulated from neuronal models comprising several common channels, we show that short (<50 ms) intracellular recordings from neurons stimulated with a complex time-varying current yield accurate and precise estimates of the model parameters as well as accurate predictions of the future behavior of the neuron. We also show that this method is robust to errors in model specification, supporting model development for biological preparations in which the channel expression and other biophysical properties of the neurons are not fully known.

RELIABILITY AND AVAILABILITY ANALYSIS OF MECHANICAL SYSTEMS USING STOCHASTIC PETRI NET MODELING BASED ON DECOMPOSITION APPROACH

Reliability and availability assessment of a complex system in a single model, considering binary states of individual components, using Markov technique is difficult due to state space explosion problem. Inclusion of various types of dependencies in the model further aggravates it. To overcome this, Stochastic Petri net (SPN) modeling based on decomposition is proposed for reliability and availability assessment of mechanical systems. The decomposition is based on three aspects of the system: Hierarchical level, basic structure and dependency. The model is demonstrated at three hierarchical levels. Individual component (level '3') SPN model is developed assuming Weibull failure distribution, while the individual subsystem (level '2') SPN model is developed considering the arrangement of components within the subsystem. The individual model at level '2' is reduced to an equivalent single net model and its equivalent transition rate is derived from its basic structure assuming the independence of components. This along with the dependencies (e.g. repair, standby redundancy) are included in the system model (level '1'). The repair distribution in this model is assumed exponential. Reachable markings are generated for the system model to obtain the reduced state space of Semi-Markov model for assessment of reliability and availability of the system. The steps of the proposed methodology are suggested and these are illustrated for a pumping system, with two pumps; one in standby.

Automatic generation of inductive invariants from high-level microarchitectural models of communication fabrics

Abstract microarchitectural models of communication fabrics present a challenge for verification. Due to the presence of deep pipelining, a large number of queues and distributed control, the state space of such models is usually too large for enumeration by protocol verification tools such as Murphi. On the other hand, we find that state-of-the-art rtl model checkers such as abc have poor performance on these models since there is very little opportunity for localization and most of the recent capacity advances in rtl model checking have come from better ways of discarding the irrelevant parts of the model. In this work we explore a new approach for verifying these models where we capture a model at a high level of abstraction by requiring that it be described using a small set of well-defined microarchitectural primitives. We exploit the high level structure present in this description, to automatically strengthen some classes of properties, in order to make them 1-step inductive, and then use an rtl model checker to prove them. In some cases, even if we cannot make the property inductive, we can dramatically reduce the number and complexity of lemmas that are needed to make the property inductive.

Flow-level performance analysis of a multi-rate system supporting stream and elastic services

SUMMARY We consider a multi-rate system where stream and elastic flows receive service. Both the stream and the elastic classes are associated with peak rate limitation. In contrast to the constant bit rate stream flows, the elastic flows tolerate bandwidth compression while in service. Because of the occasional bandwidth compression, the holding time of elastic flows depends on their perceived throughput. Although this model is Markovian under quite non-restrictive assumptions, the model's state space grows exponentially with the number of traffic classes. The model is not quasi-reversible, and therefore, it cannot be evaluated by efficient recursive formulae. We propose a method whereby the original state space is mapped to a two-dimensional one, independently of the number of the stream and the elastic traffic classes. The special structure of the two-dimensional model allows us to develop an efficient method that approximates the average throughputs of elastic flows. The state space reduction together with the proposed approximation provides a powerful tool for the performance analysis of this model as it allows the approximation of the average throughputs of elastic flows reasonably accurately in large models as well. Copyright © 2012 John Wiley & Sons, Ltd.

Strong Truncation Approximation in Tandem Queues with Blocking

Markov models are frequently used for performance modeling. However most models do not have closed form solutions, and numerical solutions are often not feasible due to the large or even infinite state space of models of practical interest. For that, the state‐space truncation is often demanded for computation of this kind of models. In this paper, we use the strong stability approach to establish analytic error bounds for the truncation of a tandem queue with blocking. Numerical examples are carried out to illustrate the quality of the obtained error bounds.

An Approach to Analyzing Time Constrained Service Composition

S ervice composition is widely applied in different applications. One key issue is how to model and analyze time-related properties for service composition. A model called service composition time-constrained Petri Net ( SCT-Net ) is proposed in the paper, which is capable of capturing time behavior of services accurately. The basic relationships, priority and preemption between services are characterized, meanwhile the transaction properties of service are also considered . In order to reduce the state space of model, we propose four simplification schemas which can maintain structural feature and time delay of SCT-Net , a theorem is given to explain the rational of simplification schemas. We present the concept of the greatest concurrent set and analyze the consistency of overtime handling based on the state space of the model. Finally, a heuristic algorithm for schedule computation is created and th e experiments are given to explain the feasibility of our method

Rate control system algorithm developed in state space for models with parameter uncertainties

researching in weightlessness above the atmosphere needs a payload to carry the experiments. To achieve the weightlessness, the payload uses a rate control system (RCS) in order to reduce the centripetal acceleration within the payload. The rate control system normally has actuators that supply a constant force when they are turned on. The development of an algorithm control for this rate control system will be based on the minimum-time problem method in the state space to overcome the payload and actuators dynamics uncertainties of the parameters. This control algorithm uses the initial conditions of optimal trajectories to create intermediate points or to adjust existing points of a switching function. It associated with inequality constraint will form a decision function to turn on or off the actuators. This decision function, for linear time-invariant systems in state space, needs only to test the payload state variables instead of spent effort in solving differential equations and it will be tuned in real time to the payload dynamic. It will be shown, through simulations, the results obtained for some cases of parameters uncertainties that the rate control system algorithm reduced the payload centripetal acceleration below µg level and keep this way with no limit cycle.

State and parameter estimation using Monte Carlo evaluation of path integrals

Transferring information from observations of a dynamical system to estimate the fixed parameters and unobserved states of a system model can be formulated as the evaluation of a discrete time path integral in model state space. The observations serve as a guiding potential working with the dynamical rules of the model to direct system orbits in state space. The path integral representation permits direct numerical evaluation of the conditional mean path through the state space as well as conditional moments about this mean. Using a Monte Carlo method for selecting paths through state space we show how these moments can be evaluated and demonstrate in an interesting model system the explicit influence of the role of transfer of information from the observations. We address the question of how many observations are required to estimate the unobserved state variables, and we examine the assumptions of Gaussianity of the underlying conditional probability.