Stochastic Automata Research Articles

Perfection of Interbudgetary Relations as a Factor of Econom-ic Growth of Depressed Miner Territories

The article is devoted to the improvement of decision-making processes in the management of inter-budgetary relations between the regions and depressed mining municipalities. The tools of decision-making support in the form of economic and mathematical models included in the control circuit are proposed. Economic and mathematical tools are based on the application of the mathematical apparatus of the theory of stochastic automata in random environments. The constructed mathematical abstraction “stochastic automaton” describes the behavior of the decision-making subject in determining the norms of shared distribution of tax revenues between budgets on the vertical line of power. A stochastic automaton possesses the property of learningability of expedient behavior. The decisions made by the automaton regarding the values of the tax revenue distribution norms are quantified through interaction with the simulation model. The simulation model forms a random environment in which the stochastic automaton is immersed, and reacts to the administrative decisions made by the automaton through its encouragement and punishment. The article proposes the construction of a stochastic automaton, described by its transition function. The transition function of an automaton from state to state is formally represented by matrices. The authors derive analytical expressions for the final probabilities of the machine in each of its states. The efficiency of the economic and mathematical tools is demonstrated through the presentation of the results of the conducted experimental studies in the selection of options for decisions regarding the share of the distribution of tax revenues.

A Novel Machine Translation Method based on Stochastic Finite Automata Model for Spoken English

Stochastic finite automata have been applied to a variety of fields, machine trans-lation is one of them. It can learn from data and build model automatically from training sets. Stochastic finite automata are well adapted for the constrained inte-gration of pairs of sentences for language processing. In this paper, a novel ma-chine translation method based on stochastic finite automata is proposed. The method formalized rational grammars by using stochastic finite automata. Through given pairs of source and target utterances, our proposed method will produce a series of conventional rules from which a stochastic rational grammar would be inferred, and the grammar is finally converted into a finite state automa-ton. The efficacy and accuracy of our proposed method is evaluated by a large number of English-Chinese and Chinese-English machine translation experi-ments.

Automated compositional importance splitting

In the formal verification of stochastic systems, statistical model checking uses simulation to overcome the state space explosion problem of probabilistic model checking. Yet its runtime explodes when faced with rare events, unless a rare event simulation method like importance splitting is used. The effectiveness of importance splitting hinges on nontrivial model-specific inputs: an importance function with matching splitting thresholds. This prevents its use by non-experts for general classes of models. In this paper, we present an automated method to derive the importance function. It considers both the structure of the model and of the formula characterising the rare event. It is memory-efficient by exploiting the compositional nature of formal models. We experimentally evaluate it in various combinations with two approaches to threshold selection as well as different splitting techniques for steady-state and transient properties. We find that Restart splitting combined with thresholds determined via a new expected success method most reliably succeeds and performs very well for transient properties. It remains competitive in the steady-state case, which is however challenging to all combinations we consider. All methods are implemented in the modes tool of the Modest Toolset and in the Fig rare event simulator. • We provide methods to automatically derive the parameters of importance splitting for rare-event simulation of formal models. • Our methods apply to a broad class of stochastic models, including Markov chains and stochastic automata. • We introduce a compositional method to derive importance functions and a new threshold selection algorithm. • We implement three different importance splitting algorithms from the literature that use these inputs. • We perform an experimental evaluation using the Modest Toolset and the FIG tool.

Detectability Measure for State Estimation of Discrete Event Systems

In this note, we investigate how to quantitatively evaluate the performance of state estimation for discrete event systems. We use a stochastic automaton to model a discrete event system. We say that an event sequence is detectable if we can determine the current and subsequent states after the occurrence of the sequence. We define the limit of the sum of probabilities of all detectable sequences when the length of the sequences goes to infinity as a quantitative indicator of goodness of state estimation. We call this indicator “detectability measure.” In order to calculate the detectability measure, we augment the discrete event system to include the information of its state estimates and then convert it into a Markov chain by removing all the event labels. Calculation of the detectability measure is then translated to calculation of the sum of probabilities of some states in the Markov chain, which can be done effectively. Finally, a practical example is used to illustrate these results.

Lumping-based equivalences in Markovian automata: Algorithms and applications to product-form analyses

In this paper we consider two relations over stochastic automata, named lumpable bisimulation and exact equivalence, that induce a strong and an exact lumping, respectively, on the underlying Markov chains. We show that an exact equivalence over the states of a non-synchronising automaton is indeed a lumpable bisimulation for the corresponding reversed automaton and then it induces a strong lumping on the time-reversed Markov chain underlying the model. This property allows us to prove that the class of quasi-reversible models is closed under exact equivalence. Quasi-reversibility is a pivotal property to study product-form models. Hence, exact equivalence turns out to be a theoretical tool to prove the product-form of models by showing that they are exactly equivalent to models which are known to be quasi-reversible. Algorithms for computing both lumpable bisimulation and exact equivalence are introduced. Case studies as well as performance tests are also presented.

Modeling of fungal mycelium growth by fourth-class continuous stochastic cellular automaton with continuously defined growth conditions

The aim of this work was to simulate the growth and spatial structure of the fungal mycelium using a cellular automaton based on the synthesis of various model approaches. The spatial structure of the mycelium is described in the structural submodel of the cellular automaton, which determines the growth rate in the direction of larger resource amount and the number of branches of the mycelium per area unit. The amount of available substrate determines the probability of unidirectional apical growth. Another, biochemical part of the model allows us to describe the rate of transport of resources into the cell, their transport within the mycelium, and also their excretion, and is intended to describe the vertical and horizontal migration in the soil of two nutrients. The proposed model makes it possible to quantitatively describe such a feature of fungal colony growth as more active absorption of resources by external cells, compared to central ones due to separation of transport resources into active and passive resources. The active transport was described using the Michaelis-Menten kinetics. We were able to simulate the stockpiling of surplus resources and their redistribution over the mycelium after the exhaustion of reserves in the external environment, and also to simulate typical growth patterns of mycelial colonies that were observed in experiments published in the literature.

Calculating All Minimal Transition-Based Sensor Activation Policies for the Purpose of Supervisory Control

Consider the problem of designing a supervisory control in which the supervisor has control not merely over the inputs (or actuators), but can also choose to turn sensors on or off. In this context, the supervisor can flexibly adjust the set of activated sensors to reduce sensor utilization without compromising the correctness of control decisions. Building upon existing methods for computing a transition-based minimal sensor activation policy, algorithms are presented in this technical note for computing all minimal transition-based sensor activation policies. This result is then extended for minimizing the numerical sensor activation cost for systems modeled by stochastic automata.

Fault Detection Algorithms based on Decomposed Tensor Representations for Qualitative Models

The paper proposes two fault detection algorithms for qualitative models based on stochastic automata. We will show that storing the transition probabilities of the stochastic automaton in tensor format enables a great potential in avoiding the major limitation of the approach - the exponential growth of the number of transitions of the automaton with an increasing number of system signals. The underlying structure of the behaviour tensor of the automaton will be exploited by CP and TT decompositions which allow a reduction in the amount of data to be stored by an order of magnitude. We will provide a proof of both algorithms and show their functionality by means of a real system example.

Correctability of fault-tolerant stochastic discrete-event systems

Failure diagnosis and correction of discrete-event systems (DESs) have received considerable attention in recent years due to the practical and theoretical importance. As a continuation of our prior work on diagnosability of stochastic DESs (i.e., Liu et al., 2008; Liu and Qiu, 2008), this paper aims to investigate the correctability issue, where the considered system is equipped with a probabilistic structure to estimate the likelihood of events occurring. More specifically: (1) We formalize the notion of k-step corrective probability to calculate the correctability of stochastic systems. Roughly speaking, the k-step corrective probability represents the probability that the stochastic system may recover to accepted states from the current state within k steps. (2) By introducing the strategy of adjusting the transition probability of the current state of system, an optimal correction mechanism is presented to achieve the maximal k-step corrective probability. (3) In addition, a novel approach of the computation of supremal corrective probability is developed by constructing the decision tree after introducing the infinitely expandable states. Finally, an example for the evolution process of the voltage in a circuit system modeled by a stochastic automaton is provided to illustrate the proposed results.

Using Stochastic Automaton for Data Consolidation

Background. Development of methods and algorithms for efficient search of relevant information on demand. The article deals with the consolidation of data for subsequent use in the information and analytical systems. Objective. The aim of the paper is to identify capabilities and build relevant information search algorithms from disparate sources by analyzing the probability information identifying the possible presence of relevant documents in these sources. Methods. To find the relevant information for search queries the approach based on the use of probability estimates of relevant documents available in the sources of further increasing the number of selected documents from these sources to analyze their relevance to the query is used. Results. A stochastic programmable automaton structure to ensure selection of the most possible information sources by relevance parameters and information retrieval algorithm based on the use of stochastic automaton were developed. Conclusions. The described algorithm using stochastic automaton for data consolidation allows developing a set of software tools, provides plenty full and holistic data consolidation problem-solving for diverse systems which search for information from information sources different in composition and presentation type.

Cost vs. time in stochastic games and Markov automata

Abstract Costs and rewards are important tools for analysing quantitative aspects of models like energy consumption and costs of maintenance and repair. Under the assumption of transient costs, this paper considers the computation of expected cost-bounded rewards and cost-bounded reachability for Markov automata and Markov games. We provide a fixed point characterization of this class of properties under early schedulers. Additionally, we give a transformation to expected time-bounded rewards and time-bounded reachability, which can be computed by available algorithms. We prove the correctness of the transformation and show its effectiveness on a number of Markov automata case studies.

An adaptive trust-Stackelberg game model for security and energy efficiency in dynamic cognitive radio networks

Due to the potential of cooperative cognitive radio networks (CCRNs) in addressing the spectrum scarcity problem in wireless communication networks, CCRN has become a subject of active research. For example, security and energy efficiency are two salient areas of research in CCRNs. In this paper, we propose a novel adaptive trust-Stackelberg game model designed to (a) improve the energy efficiency and (b) defend against insider attacks in CCRNs. More specifically, the distributed learning algorithm (DLA) for the relays in our model, inspired by the stochastic learning automata, allows the system to achieve Stackelberg equilibrium in the proposed game; and the trust evolution based on evolutionary stable strategy algorithm (TEEA) allows the primary user to defend against insider attacks efficiently and adaptively adjust the trust evolution in dynamic CCRNs. We demonstrate the utility of the proposed model comparing with other models using a numerical investigation. The numerical results show that the proposed model can improve the performance in energy efficiency and defending against insider attacks with an appropriate cooperation between primary users and relays.

Cycle bases of reduced powers of graphs

We define what appears to be a new construction. Given a graph G and a positive integer k , the reduced k th power of G , denoted G ( k ) , is the configuration space in which k indistinguishable tokens are placed on the vertices of G , so that any vertex can hold up to k tokens. Two configurations are adjacent if one can be transformed to the other by moving a single token along an edge to an adjacent vertex. We present propositions related to the structural properties of reduced graph powers and, most significantly, provide a construction of minimum cycle bases of G ( k ) . The minimum cycle basis construction is an interesting combinatorial problem that is also useful in applications involving configuration spaces. For example, if G is the state-transition graph of a Markov chain model of a stochastic automaton, the reduced power G ( k ) is the state-transition graph for k identical (but not necessarily independent) automata. We show how the minimum cycle basis construction of G ( k ) may be used to confirm that state-dependent coupling of automata does not violate the principle of microscopic reversibility, as required in physical and chemical applications.

Simple stochastic cellular automaton model for starved beds and implications about formation of sand topographic features in terms of sand flux

A simple stochastic cellular automaton model is proposed for simulating bedload transport, especially for cases with a low transport rate and where available sediments are very sparse on substrates in a subaqueous system. Numerical simulations show that the bed type changes from sheet flow through sand patches to ripples as the amount of sand increases; this is consistent with observations in flume experiments and in the field. Without changes in external conditions, the sand flux calculated for a given amount of sand decreases over time as bedforms develop from a flat bed. This appears to be inconsistent with the general understanding that sand flux remains unchanged under the constant-fluid condition, but it is consistent with the previous experimental data. For areas of low sand abundance, the sand flux versus sand amount (flux–density relation) in the simulation shows a single peak with an abrupt decrease, followed by a long tail; this is very similar to the flux–density relation seen in automobile traffic flow. This pattern (the relation between segments of the curve and the corresponding bed states) suggests that sand sheets, sand patches, and sand ripples correspond respectively to the free-flow phase, congested phase, and jam phase of traffic flows. This implies that sand topographic features on starved beds are determined by the degree of interference between sand particles. Although the present study deals with simple cases only, this can provide a simplified but effective modeling of the more complicated sediment transport processes controlled by interference due to contact between grains, such as the pulsatory migration of grain-size bimodal mixtures with repetition of clustering and scattering.

Fault Detection with CP-Decomposed Qualitative Models

The paper shows how a fault detection algorithm based on stochastic automata as qualitative model can be improved by non-negative CP tensor decomposition to make it applicable to large discrete-time systems. Because exponential growth of the number of transitions of the automaton with a rising number of states, inputs and outputs of the system can usually not be avoided, tensor decomposition methods enable the reduction of the amount of data to be stored by an order of magnitude. In order to exploit the full potential of the decomposition, a fault detection algorithm that is applicable to the decomposed tensor structure is defined. An example based on real measurement data shows the functionality of the algorithm.

Stochastic Polling Interval Adaptation in Duty-Cycled Wireless Sensor Networks

In past decades, to achieve energy-efficient communication, many MAC protocols have been proposed for wireless sensor networks (WSNs). Particularly, asynchronous MAC protocol based on low power listening (LPL) scheme is very attractive in duty-cycled WSNs: it reduces the energy wasted by idle listening. In LPL scheme, a sensor node wakes up at every polling interval to sample the channel. If the channel is busy, the sensor node will stay in wake-up mode for receiving the data packet. Otherwise, it goes to sleep and saves power. However, wrong choice of polling interval in LPL scheme causes unexpected energy dissipation. This paper focuses on the polling interval adaptation strategy in LPL scheme with the aim of maximizing energy efficiency, defined as the number of packets delivered per energy unit. We propose a novel polling interval adaptation algorithm based on stochastic learning automata, where a sensor node dynamically adjusts its polling interval. Furthermore, our simulation results demonstrate that the polling interval asymptotically converges to the optimal value.

Fault Detection with Qualitative Models reduced by Tensor Decomposition methods

The paper shows how a fault diagnosis algorithm based on stochastic automata as qualitative models can be improved by tensor decomposition methods to make it applicable to complex discrete-time systems. While exponential growth of the number of transitions of the automaton with the number of states, inputs and outputs of the system can in principle not be avoided, matrix representations of the automaton can be reduced by exploiting the underlying tensor structure of the behaviour relation. For non-negative CP tensor decomposition, algorithms are available that can be tuned by defining an order of the approximation. The example of a heat exchanger shows the applicability of the proposed method in situations where real measurement data of the nominal behaviour are available and the modelling effort has to be small.

Стохастическое клеточно-автоматное моделирование колебаний и автоволн в реакционно-диффузионных системах

Стохастическое клеточно-автоматное моделирование колебаний и автоволн в реакционно-диффузионных системах

Spatial Spread of Tuberculosis through Neighborhoods Segregated by Socioeconomic Position: A Stochastic Automata Model

Transmission of the agent of tuberculosis,Mycobacterium tuberculosis, is dependent on social context. A discrete spatial model representing neighborhoods segregated by levels of crowding and immunocompetence is constructed and used to evaluate prevention strategies, based on a number of assumptions about the spatial dynamics of tuberculosis. A cellular automata model is used to (a) construct neighborhoods of different densities, (b) model stochastically local interactions among individuals, and (c) model the spread of tuberculosis within and across neighborhoods over time. Since infected people may become progressively sick but also heal through treatment, the transition among stages was modeled with transition probabilities. A moderate level of successful treatment (40%) dramatically reduced the number of infections across all neighborhoods. Increasing the treatment in neighborhoods of a lower socioeconomic level from 40% to 90% results in an additional decrease of approximately 25% in the number of infected individuals overall. In conclusion, we find that a combination of a moderate level of successful treatment across all areas with more focused treatment efforts in lower socioeconomic areas resulted in the least number of infections over time.

Application of stochastic automata networks for creation of continuous time Markov chain models of voltage gating of gap junction channels.

The primary goal of this work was to study advantages of numerical methods used for the creation of continuous time Markov chain models (CTMC) of voltage gating of gap junction (GJ) channels composed of connexin protein. This task was accomplished by describing gating of GJs using the formalism of the stochastic automata networks (SANs), which allowed for very efficient building and storing of infinitesimal generator of the CTMC that allowed to produce matrices of the models containing a distinct block structure. All of that allowed us to develop efficient numerical methods for a steady-state solution of CTMC models. This allowed us to accelerate CPU time, which is necessary to solve CTMC models, ∼20 times.