Probabilistic Automata Research Articles

Modeling of Steel Production Sub-Processes by Probabilistic Time Automaton and Assessing the Risk of Deviation from Stability in the Manufacturing Facility Environment

Modeling of Steel Production Sub-Processes by Probabilistic Time Automaton and Assessing the Risk of Deviation from Stability in the Manufacturing Facility Environment

Automatic activity-travel sequence generator using language, grammar, and machine theory

ABSTRACT Activity schedule results from a complex decision-making process characterized by several interrelated decisions. Different facets of an activity schedule such as activity type, timing, duration, etc. influence each other and this makes modeling activity schedules a complex task. This complexity has compelled researchers to explore different approaches for modeling activity schedules, among which two predominant approaches can be identified: the utility-maximization theory based econometric approach and the computational process modeling approach. Despite their advantages and a few successful practical applications, challenges still remain leaving avenues for exploration of new approaches. This paper contributes in this direction by reviewing the relationship between language, grammar, and machines in the context of sequence analysis for activity sequence generation. Following that, the paper presents a stochastic Finite State Machine that can generate activity sequences to match the frequency distribution of sequences from a given data set. Our results show that the proposed algorithm can not only generate activity sequences with a distribution similar to that of original data but can also efficiently generate new patterns not in the original data.

Survival and Evolutionary Adaptation of Populations Under Disruptive Habitat Change: A Study With Darwinian Cellular Automata.

The evolution of living beings with continuous and consistent progress toward adaptation and ways to model evolution along principles as close as possible to Darwin's are important areas of focus in Artificial Life. Though genetic algorithms and evolutionary strategies are good methods for modeling selection, crossover, and mutation, biological systems are undeniably spatially distributed processes in which living organisms interact with locally available individuals rather than with the entire population at once. This work presents a model for the survival of organisms during a change in the environment to a less favorable one, putting them at risk of extinction, such as many organisms experience today under climate change or local habitat loss or fragmentation. Local spatial structure of resources and environmental quality also impacts the capacity of an evolving population to adapt. The problem is considered on a probabilistic cellular automaton with update rules based on the principles of genetic algorithms. To carry out simulations according to the described model, the Darwinian cellular automata are introduced, and the software has been designed with the code available open source. An experimental evaluation of the behavioral characteristics of the model was carried out, completed by a critical evaluation of the results obtained, parametrically describing conditions and thresholds under which extinction or survival of the population may occur.

Persistence of spectral projections for stochastic operators on large tensor products

Abstract It is proved that for families of stochastic operators on a countable tensor product, depending smoothly on parameters, any spectral projection persists smoothly, where smoothness is defined using norms based on ideas of Dobrushin. A rigorous perturbation theory for families of stochastic operators with spectral gap is thereby created. It is illustrated by deriving an effective slow two-state dynamics for a three-state probabilistic cellular automaton.

Particle Swarm Optimization-Based Model Abstraction and Explanation Generation for a Recurrent Neural Network

In text classifier models, the complexity of recurrent neural networks (RNNs) is very high because of the vast state space and uncertainty of transitions, which makes the RNN classifier’s explainability insufficient. It is almost impossible to explain the large-scale RNN directly. A feasible method is to generalize the rules undermining it, that is, model abstraction. To deal with the low efficiency and excessive information loss in existing model abstraction for RNNs, this work proposes a PSO (Particle Swarm Optimization)-based model abstraction and explanation generation method for RNNs. Firstly, the k-means clustering is applied to preliminarily partition the RNN decision process state. Secondly, a frequency prefix tree is constructed based on the traces, and a PSO algorithm is designed to implement state merging to address the problem of vast state space. Then, a PFA (probabilistic finite automata) is constructed to explain the RNN structure with preserving the origin RNN information as much as possible. Finally, the quantitative keywords are labeled as an explanation for classification results, which are automatically generated with the abstract model PFA. We demonstrate the feasibility and effectiveness of the proposed method in some cases.

Correction to “Current-State Opacity Formulations in Probabilistic Finite Automata”

Correction to “Current-State Opacity Formulations in Probabilistic Finite Automata”

Protecting information via probabilistic cellular automata.

Probabilistic cellular automata describe the dynamics of classical spin models, which, for sufficiently small temperature T, can serve as classical memory capable of storing information even in the presence of nonzero external magnetic field h. In this article, we study a recently introduced probabilistic cellular automaton, the sweep rule, and map out a region of two coexisting stable phases in the (T,h) plane. We also find that the sweep rule belongs to the weak two-dimensional Ising universality class. Our work is a step towards understanding how simple geometrically local error-correction strategies can protect information encoded into complex noisy systems, such as topological quantum error-correcting codes.

A refined simulation method of building earthquake evacuation processes considering multi-exits and time-variant velocities

This study proposes a refined method for effectively simulating the evacuation processes of multi-story buildings during earthquakes. The method is developed by combining the exit-option algorithm and multi-velocity field model with the previously developed probabilistic network-based floor-field cellular automaton (PN-FFCA) model. Besides, the formula is also proposed for calculating the time-variant moving velocities of evacuees in the buildings subjected to the earthquake loads. Consequently, the refined method can fully consider the effect of multi-exits and time-variant velocities on the random evacuation processes of multi-story buildings during earthquakes. The recorded evacuation process of a school classroom during the 2022 Luding earthquake in China is reproduced using the refined method, which verifies its validity. In addition, the evacuation processes of an actual three-story office building subjected to random earthquake loads are simulated using the refined method. The simulated results are compared with those obtained from the PN-FFCA to demonstrate the advantages and utility of the refined method.

Non-Intrusive Load Identification of Residential Appliances Using Improved Dictionary Learning Technique

With the advent of time, the demand for power in the residential sector is increasing. Along with supply-side management, the demand side is also used to balance electricity and supply demand. To apply different demand-side management techniques, the energy disaggregation on metered data is used to retrieve information related to available demand. Non-intrusive load monitoring is a technique that separates the total power consumption into appliance loads with minimum invasion of privacy. Non-intrusive load monitoring covers the methods of Stochastic finite state machines, Neural Networks and Sparse Coding. Developing an efficient algorithm for NILM is a key challenge in maximizing energy conservation. Recently, a new deep learning technique called dictionary learning has been developed for energy disaggregation. Smart meters provide the whole house data, and the Dictionary technique is trained to predict an appliance's power or ON/OFF based on its power consumption. This research proposes the event-based dictionary learning technique, which can disaggregate multiple appliances through orthogonal matching pursuit (OMP) and kernel-singular value decomposition (K-SVD). The sparse matrix is predicted through OMP, and K-SVD predicts the dictionary matrix. The training, testing and validation are done on the ECO dataset. The results of this research are noticeable and show the validity of the proposed methodology for energy disaggregation.

Verification and Enforcement of (ϵ, ξ)-Differential Privacy over Finite Steps in Discrete Event Systems

In the realm of data protection strategies, differential privacy ensures that unauthorized entities cannot reconstruct original data from system outputs. This study explores discrete event systems, specifically through probabilistic automata. Central is the protection of state data, particularly the initial state privacy of multiple starting states. We introduce an evaluation criterion to safeguard initial states. Using advanced algorithms, the proposed method counters the probabilistic identification of any state within this collection by adversaries from observed data points. The efficacy is confirmed when the probability distributions of data observations tied to these states converge. If a system’s architecture does not meet state differential privacy demands, we propose an enhanced supervisory control mechanism. This control upholds state differential privacy across all initial states, maintaining operational flexibility within the probabilistic automaton framework. Concluding, a numerical analysis validates the approach’s strength in probabilistic automata and discrete event systems.

Lifting query complexity to time-space complexity for two-way finite automata

Time-space tradeoff has been studied in a variety of models, such as Turing machines, branching programs, and finite automata, etc. While communication complexity as a technique has been applied to study finite automata, it seems it has not been used to study time-space tradeoffs of finite automata. We design a new technique showing that separations of query complexity can be lifted, via communication complexity, to separations of time-space complexity of two-way finite automata. As an application, one of our main results exhibits the first example of a language L such that the time-space complexity of two-way probabilistic finite automata with a bounded error (2PFA) is Ω˜(n2), while of exact two-way quantum finite automata with classical states (2QCFA) is O˜(n5/3), that is, we demonstrate for the first time that exact quantum computing has an advantage in time-space complexity comparing to classical computing.

ANALYSIS OF CHANGES IN FRACTAL, STATISTICAL AND KINETIC PARAMETERS DURING THE HETEROANNIHILATION OF PARTICLES ON THE SIMULATED STRUCTURALLY INHOMOGENEOUS SURFACES

To investigate the mechanisms of interaction of particles on structurally inhomogeneous surfaces, the influence of surface morphology, distribution of interacting particles and their mobility on the mechanisms of ongoing processes, various modeling approaches are widely used. The paper presents the results of comparison of kinetic, statistical and fractal parameters changing in the process of heteroannihilation of particles distributed chaotically and multifractally on a simulated structurally inhomogeneous surface. To simulate the complex behavior of particles in time and space during heteroannihilation with changes in their mobility across the surface and various interaction probabilities, a class IV probabilistic cellular automaton method was applied. Based on the simulation results, it is shown that the interaction probability, initial distribution, and mobility of interacting particles influence the formation of kinetic modes at different iterations of the heteroannihilation process. It was found that a decrease in the mobility of interacting particles leads to a longer preservation of spatial heterogeneity in the system. An increase in the mobility of interacting particles and the probability of their interaction increases the rate of change in the fractal dimensionality and the rate coefficients of heteroannihilation kinetics. Decrease of fractal dimensionality during heteroannihilation is accompanied by decrease of asymmetry and increase of excess characterizing shape and degree of symmetry of distribution of interacting particles. At the same time, large values of asymmetry and excess indicate a significant deviation from the normal distribution of interacting particles on the surface.

Towards a model of human-cyber–physical automata and a synthesis framework for control policies

Advances in research and increasing applications of Cyber–Physical Systems (CPSs) show the need to consider factors of humans in the loop. This has led to the growing research focus on Human-Cyber–Physical Systems (HCPSs). In general, humans in an HCPS interact with both the cyber and physical systems, as well as among the humans themselves. For a better understanding, correct design, development, operation, and maintenance of HCPSs, a computational theory based on a computational model is required. This paper presents our initial work towards a model of human-cyber–physical automata (HCPA). We consider an HCPS as a combination of a human-physical system (HPS) and a CPS in which the control switches between the humans and the machines. We define an HCPA by connecting the automaton of the HPS and the automaton of the CPS through a switch control automaton. The switch control automaton makes switching decision in some critical states shared by the HPS and the CPS. Our theorem shows that the control switching between the HPS and the CPS increases the probability of satisfying a given property. We model the behaviour of a human in specified applications or even in carry out specific tasks, instead of general human intelligence. Therefore, a human can make mistakes to decision making and thus it is a probabilistic automaton with learning ability. The switching between the human and the machine is modelled by an oracle. The oracle learns about the human behaviour, the machine behaviour, as well as the environment to make the control decisions. To generate the control policies of the human and the oracle, we propose a synthesis framework to maximize the probability of the satisfaction of a property specified in Linear Temporal Logic (LTL) by the HCPA. We present a prototype implementation of the framework by extending the model-free reinforcement learning (RL) algorithm and model-free deep-RL algorithm, and our experiment shows that our synthesis framework is effective in obtaining switch policies.

System reduction: an approach based on probabilistic cellular automata

System reduction: an approach based on probabilistic cellular automata

Floquet Codes without Parent Subsystem Codes

We propose a new class of error-correcting dynamic codes in two and three dimensions that has no explicit connection to any parent subsystem code. The two-dimensional code, which we call the CSS (Calderbank-Shor-Steane) honeycomb code, is geometrically similar to that of the honeycomb code by Hastings and Haah and also dynamically embeds an instantaneous toric code. However, unlike the honeycomb code, it possesses an explicit CSS structure and its gauge checks do not form a subsystem code. Nevertheless, we show that our dynamic protocol conserves logical information and possesses a threshold for error correction. We generalize this construction to three dimensions and obtain a code that fault tolerantly alternates between realizing two type-I fracton models, the checkerboard and the X-cube model. Finally, we show the compatibility of our CSS honeycomb-code protocol and the honeycomb code by showing the possibility of randomly switching between the two protocols without information loss while still measuring error syndromes. We call this more general aperiodic structure “dynamic tree codes,” which we also generalize to three dimensions. We construct a probabilistic finite automaton prescription that generates dynamic tree codes correcting any single-qubit Pauli errors and can be viewed as a step toward the development of practical fault-tolerant random codes.1 MoreReceived 27 December 2022Accepted 21 April 2023DOI:https://doi.org/10.1103/PRXQuantum.4.020341Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum error correctionQuantum memoriesSurface code quantum computingTopological orderTopological phases of matterQuantum Information

Modeling Exact Frequency-Energy Distribution for Quakes by a Probabilistic Cellular Automaton.

We develop the notion of Random Domino Automaton, a simple probabilistic cellular automaton model for earthquake statistics, in order to provide a mechanistic basis for the interrelation of Gutenberg-Richter law and Omori law with the waiting time distribution for earthquakes. In this work, we provide a general algebraic solution to the inverse problem for the model and apply the proposed procedure to seismic data recorded in the Legnica-Głogów Copper District in Poland, which demonstrate the adequacy of the method. The solution of the inverse problem enables adjustment of the model to localization-dependent seismic properties manifested by deviations from Gutenberg-Richter law.

Detection of anomalies of a non-deterministic software-defined networking control

Software Defined Networking (SDN) is a network architecture within the control is centralized through a software-based controller. Being a single point of attack makes the controller the preferred target in the SDN architecture. Multi-controller architecture has been introduced to reinforce the control plane. However it requires a communication interface between the controllers which is a security threat. In this objective, a dual controller architecture is introduced and it consists of one nominal controller in charge of the data plane computation plus a second one in charge of the detection of anomalies in the decisions taken by the main controller. In the case of non-determinist algorithm, the detection logic aims at determining a likelihood score of the decisions taken by the controller. A multi-criterion detection approach is proposed by considering both the performance of the decisions and the structure of the decisions taken by the controller. Such computations are probabilistic and attention has been paid to machine learning algorithms to determine this likelihood. More precisely, three formalisms are compared: Probabilistic Finite Automaton, Hidden Markov Model and Recurrent Neural Network. The impact of the control variance in the detection accuracy depending on the formalism used is discussed on a case study.

Optimization of a recurrent neural network using automata with a variable structure

The subject of this study is to identify a set of common structural properties inherent in recurrent neural networks and stochastic automata, the feature of which is purposeful behavior in dynamic environments. At the same time, the necessary commonality of properties is revealed both in the process of their functioning and in the process of their training (tuning). The author considers in detail such topics as: formalization of purposeful behavior, consideration of the design of automata, as well as a comparative analysis of the considered designs of automata. From the revealed commonality of functioning and the established one-to-one correspondence of neurons of a fully connected recurrent neural network and states of a probabilistic automaton with a variable structure, it follows that the structure of a tuned stochastic automaton can be considered as a reference for a set of connections of a recurrent neural network. This leads, even at the setup stage, to the removal of redundant states (neurons) and connections between them, based on the parameters of the corresponding automaton. The methodology of the conducted research is the construction of a one-to-one correspondence between the neurons of a fully connected recurrent neural network and the internal states of an automaton with a variable structure and the probabilities of transitions between them that are relevant after the tuning process. With a one-to-one correspondence, the probabilities of transitions of the automaton correspond to the weights of connections between neurons of the optimal configuration. The main conclusions of the study: 1.Comparing the structures of recurrent neural networks and automata with a variable structure allows one to take advantage of an automaton with a variable structure to solve the problem of appropriate behavior in dynamic environments and build a recurrent neural network based on it; 2.The correspondence of the internal structure of a recurrent neural network and an automaton with a variable structure allows already at the training stage to release the trained recurrent neural network from redundant neurons and redundant connections in its structure; 3.Due to the fact that an automaton with a variable structure approaches the optimal automaton with linear tactics for these conditions with nonlinear values of the learning rate, this allows a logical analysis of the structure of the final recurrent neural network.

Equivalence between finite state stochastic machine, non-dissipative and dissipative tight-binding and Schrödinger model

The mathematical equivalence between finite state stochastic machine and non-dissipative and dissipative quantum tight-binding and Schrödinger model is derived. Stochastic Finite state machine is also expressed by classical epidemic model and can reproduce the quantum entanglement emerging in the case of electrostatically coupled qubits described by von-Neumann entropy both in non-dissipative and dissipative case. The obtained results show that quantum mechanical phenomena might be simulated by classical statistical model as represented by finite state stochastic machine. It includes the quantum like entanglement and superposition of states. Therefore coupled epidemic models expressed by classical systems in terms of classical physics can be the base for possible incorporation of quantum technologies and in particular for quantum like computation and quantum like communication. The classical density matrix is derived and described by the equation of motion in terms of anticommutator. Existence of Rabi like oscillations is pointed in classical epidemic model. Furthermore, the existence of Aharonov–Bohm effect in quantum systems (Becker et al., 2019) can also be reproduced by the classical epidemic model or in broader sense by finite state stochastic machine. Every quantum system made from quantum dots and described by simplistic tight-binding model by use of position-based qubits can be effectively described by classical statistical model encoded in finite stochastic state machine with very specific structure of S matrix that has twice bigger size as it is the case of quantum matrix Hamiltonian. Furthermore, the description of linear and non-linear stochastic finite state machine is mapped to tight-binding and Schrödinger model. The concept of N dimensional complex time is incorporated into tight-binding model, so the description of dissipation in most general case is possible. Obtained results help in approximation of non-dissipative or dissipative quantum mechanical phenomena by classical statistical physics expressed by finite state stochastic machine. Furthermore, the equivalence of Wannier tight-binding dissipative or non-dissipative formalism to dissipative or non-dissipative Schrödinger formalism and to finite state stochastic machine was shown.

Implementation of a Model-Oriented Approach for Supporting Safe Integration of GNSS-Based Virtual Balises in ERTMS/ETCS Level 3

Moving Block is a railway signaling concept that paves the way for increasing line capacity while reducing maintenance and operating costs. Its implementation relies on autonomous solutions for train localization, mainly based on GNSS technology. However, the introduction of such technological innovations leads to the emergence of new risks. These risks need to be investigated meticulously, and some confidence level needs to be assigned to GNSS-based localization solutions in railways while considering various settings. The contribution of this paper falls within this context by bringing formal approaches into play in order to evaluate performance and safety properties related to the use of GNSS-based virtual balises for train localization. Specifically, the adopted model-based approach consists in translating the relevant behavior of the localization system through configurable timed and probabilistic automata. The elaborated models being parameterizable, various test scenarios, considering a wide range of configurations, can be investigated. Quantitative and qualitative analysis results can be generated on the basis of our models by means of statistical model-checking algorithms implemented in the UPPAAL-SMC modeling and verification tool. A case study is used to illustrate the application of the presented approach, and various numerical analysis results are provided. As the present contribution implements a model-driven approach to perform safety analysis in railways, it is fully in line with the increasing willingness to reduce recourse to on-site tests in the sector. Such tests are indeed costly and time-consuming, thus jeopardizing the introduction of technical innovations in railways.