State Automata Research Articles

Automata for knowledge assessment based on the structure of observed learning outcome taxonomy

The process of adaptive assessment of individuals' knowledge by knowledge space theory has been implemented in deterministic finite automata. However, such automata are not suitable for polytomous situations, which limits the application of automata for knowledge assessment. To overcome this limitation, this paper combines the structure of observed learning outcome (SOLO) taxonomy with the response scale and proposes an automata knowledge assessment process that can assess individuals' knowledge in polytomous situations. Specifically, an automaton suitable for assessing knowledge in the SOLO taxonomy situation is proposed, and a questioning rule is provided based on the quasi-order relation between items. Then, relying on the automaton state update and the questioning rule, an automata knowledge assessment process for knowledge assessment in the SOLO taxonomy situation is given. Finally, empirical research and simulation experiments show that it is necessary to provide a questioning rule for the automaton and that the automata knowledge assessment process proposed in this paper is feasible.

Crash-Resilient Decentralized Synchronous Runtime Verification

<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Runtime verification</i> is a technique, where a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">monitor</i> process extracts information from a running system in order to evaluate whether system executions violate or satisfy a given correctness specification. In this paper, we consider runtime verification of synchronous distributed systems, where a set of decentralized monitors that only have a partial view of the system are subject to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">crash failures</i> . In this context, it is unavoidable that monitors may have different views of the underlying system, and, therefore, have different opinions about the correctness property. We propose an automata-based synchronous monitoring algorithm that copes with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$t$</tex-math></inline-formula> crash monitor failures. In our proposed approach, local monitors do not communicate their explicit reading of the underlying system. Rather, they emit a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">symbolic verdict</i> that efficiently encodes their partial views. This significantly reduces the communication overhead. To this end, we also introduce an (offline) SMT-based monitor synthesis algorithm, which results in minimizing the size of monitoring messages. We evaluate our algorithm on a wide range of formulas and observe an average of 2.5 times increase in the number of states of the monitor automaton.

Minimization of hesitant L-fuzzy automaton

In this paper, we study a new generalization for the notion of fuzzy automata, which we called hesitant L-fuzzy automaton (HLFA). We present the formulations of the mathematics framework for the theory of HLFA. Moreover, we present the concepts of hesitant L-fuzzy behavior and inverse hesitant L-fuzzy behavior recognized by a type of HLFA. After that, for any hesitant L-fuzzy language we present a minimal complete accessible deterministic hesitant L-fuzzy automaton recognizing that. Finally, we present an algorithm, which determines states of the minimal hesitant L-fuzzy automaton and we present the time complexity of the algorithm.

Co-lexicographically Ordering Automata and Regular Languages - Part I

The states of a finite-state automaton 𝒩 can be identified with collections of words in the prefix closure of the regular language accepted by 𝒩. But words can be ordered, and among the many possible orders a very natural one is the co-lexicographic order. Such naturalness stems from the fact that it suggests a transfer of the order from words to the automaton’s states. This suggestion is, in fact, concrete and in a number of articles automata admitting a total co-lexicographic ( co-lex for brevity) ordering of states have been proposed and studied. Such class of ordered automata — Wheeler automata — turned out to require just a constant number of bits per transition to be represented and enable regular expression matching queries in constant time per matched character. Unfortunately, not all automata can be totally ordered as previously outlined. In the present work, we lay out a new theory showing that all automata can always be partially ordered, and an intrinsic measure of their complexity can be defined and effectively determined, namely, the minimum width p of one of their admissible co-lex partial orders –dubbed here the automaton’s co-lex width . We first show that this new measure captures at once the complexity of several seemingly-unrelated hard problems on automata. Any NFA of co-lex width p : (i) has an equivalent powerset DFA whose size is exponential in p rather than (as a classic analysis shows) in the NFA’s size; (ii) can be encoded using just Θ(log p ) bits per transition; (iii) admits a linear-space data structure solving regular expression matching queries in time proportional to p 2 per matched character. Some consequences of this new parameterization of automata are that PSPACE-hard problems such as NFA equivalence are FPT in p , and quadratic lower bounds for the regular expression matching problem do not hold for sufficiently small p . Having established that the co-lex width of an automaton is a fundamental complexity measure, we proceed by (i) determining its computational complexity and (ii) extending this notion from automata to regular languages by studying their smallest-width accepting NFAs and DFAs. In this work we focus on the deterministic case and prove that a canonical minimum-width DFA accepting a language ℒ–dubbed the Hasse automaton ℋ of ℒ–can be exhibited. ℋ provides, in a precise sense, the best possible way to (partially) order the states of any DFA accepting ℒ, as long as we want to maintain an operational link with the (co-lexicographic) order of ℒ’s prefixes. Finally, we explore the relationship between two conflicting objectives: minimizing the width and minimizing the number of states of a DFA. In this context, we provide an analogue of the Myhill-Nerode Theorem for co-lexicographically ordered regular languages.

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.

Joint low power state assignment of sequential automata of a net implementing a parallel automaton

Objectives. The problem of low power state assignment of partial states of a parallel automaton is considered. The objective of the paper is to investigate the possibilities of using the decomposition in state assignment of partial states in order to decrease the task dimension.Methods. Parallel automaton is decomposed into a net of sequential automata whose states are assigned then with ternary vectors. The method for assignment uses searching for a maximal cut in a weighted graph that represents pairs of states connected by transitions. The edge weights of the graph are the values related to the probabilities of transitions.Results. A method to construct a net of sequential automata that realizes the given parallel automaton is described. The probabilities of transitions between sets are calculated by means of solving a system of linear equations according to the Chapmann – Kolmogorov method. The values of inner variables assigned to the states of every component sequential automaton are obtained from two-block partitions of its set of states that are determined by the cuts of corresponding transition graph.Conclusion. Applying parallel automaton decomposition allows decreasing the dimension of the laborious problem of state assignment. The proposed method is intended for application in computer aided systems for design of discrete devices.

Ordering regular languages and automata: Complexity

Given an order of the underlying alphabet, we can lift it to the states of a finite deterministic automaton: to compare states we use the order of the strings reaching them. When the order on strings is the co-lexicographic one and this order turns out to be total, the DFA is called Wheeler. This recently introduced class of automata—the Wheeler automata—constitute an important data-structure for languages, since it allows the design and implementation of a very efficient tool-set of storage mechanisms for the transition function, supporting a large variety of substring queries.In this context it is natural to consider the class of regular languages accepted by Wheeler automata, i.e. the Wheeler languages. An inspiring result in this area is the following: it has been shown that, as opposed to the general case, the classic determinization by powerset construction is polynomial on Wheeler automata. As a consequence, most classical problems, when considered on this class of automata, turn out to be “easy”—that is, solvable in polynomial time.In this paper we consider computational problems related to Wheelerness, but starting from non-deterministic automata. We also consider the case of reduced non-deterministic ones—a class of NFAs where recognizing Wheelerness is still polynomial, as for DFAs. Our collection of results shows that moving towards non-determinism is, in most cases, a dangerous path leading quickly to intractability.Moreover, we start a study of “state complexity” related to Wheeler DFAs and languages, proving that the classic construction for the intersection of languages turns out to be computationally simpler on Wheeler DFAs than in the general case. We also provide a construction for the minimum Wheeler DFA recognizing a given Wheeler language.

Метод комплексного контроля передачи трафика в программно-конфигурируемых сетях

Modern requirements for traffic processing should possess the properties of mobility, speed, and simplification of network equipment administration. However, the existing classical Ethernet networks with Quality of Service failed to meet these requirements, which led to the emergence of software defined networks (SDN). In SDN, the main protocol is OpenFlow, which enables processing and managing heterogeneous traffic. This article aims to propose a methodology for eliminating the disadvantages inherent in the OpenFlow protocol. A method for complex control of traffic transmission in SDN was developed based on the algorithm of early diagnosis of real-time traffic losses during the transmission of heterogeneous traffic in the OpenFlow switch and the algorithm of real-time traffic transmission using a scheduler and a delivery control function in SDN. Moore digital automata of the proposed transmission algorithms were developed. A description of systems of canonical equations and output functions for digital automata was presented. Tables of transitions of digital automata were constructed, states of digital automata were encoded, and digital automata were synthesized based on D-triggers. The formalization of the developed method and algorithms of traffic transmission in SDN based on digital automata made it possible to design control automata and algorithms on FPGA of the Spartan 6 family and later familie.

ON THE THEORY OF SYNTHESIS OF MINIMAL SCHEMES OF SYSTEMS CONTROL OF HYDRAULIC AND PNEUMATIC DRIVES

Showed the strict compliance of the scientific direction "Synthesis of minimum control schemes of hydraulic and pneumatic drive systems" developed by the author with the point of view of general algebra, algebra of logic, graph theory and automata theory. The synthesis of the minimum graph of operations, which is a mathematical model of the control system, has been proved. The legitimacy of the methods of undivided decomposition of equations describing the scheme of the control system has been proved. The control system is considered as a cyclic Moore finite automaton. By a cyclic automaton (CA) we will understand the mathematical model of a device designed to control cyclic processes, which are a set of technological operations performed in a certain sequence. In this regard, the automaton at each clock necessarily passes into some new state, and for a finite number of cycles the target reaches any state, and its graph contains a contour, covering all states. In general, the CA may contain several circuits, so that each circuit is interpreted either as one of the possible sequences of technological operations due to the corresponding mode of operation, or as an independent and simultaneous execution of a number of sets of technological operations. A sequential decomposition of the CA is presented in order to represent it by the sequential operation of automata with one internal state. Such a consideration of the function of transitions will naturally lead to a decrease in the number of elements in the implementation of the CA. The study will be subjected to the CA, the graph of which consists of a single circuit, since the results obtained are easily generalized to multi-circuit CA. Obtaining a breakdown of the states of a cyclic automaton in the manner indicated above is performed directly according to any automaton description without any additional calculations, tables and other constructions.

Selection of Intelligent Rules for the Evolution of Elementary Cellular Automata for Image Encryption

The paper is devoted to the search for new approaches to the formation of key arrays for encryption of color images. Emphasis is placed on using the initial key sequence of the smallest length. In this case, the key is the initial state of an elementary cellular automaton for implementing evolution based on a given rule. The use of an evolutionary approach on cellular automata to the formation of large key arrays made it possible to achieve unpredictable image encryption based on a single rule of an elementary cellular automata. The task of the research is to search for the rules of elementary cellular automata, which, based on a small initial key bit sequence, allow one to form a reliable key array of large dimensions for encrypting the bit layers that make up the image. To solve this problem, an experiment was carried out, on the basis of which the search for the necessary rules and options for choosing the elements of each bit array was carried out to encrypt the bit layers of the image. To form each bit key array, different initial conditions were used for elementary cellular automata. It is shown that for different initial conditions and for the chosen rules, the encryption quality is preserved. The most reliable encryption is the use of two key arrays formed on the basis of the evolution of one rule for different initial conditions. As a result of the experiments, the rules were determined (rules 90, 105, 150 and XOR function based on the two previous steps of evolution), which can be used without additional rules. Each bit layer of the image is encrypted using different subarrays of each generated one key array of the same dimension. It has been established that the most effective for encryption is the rule 105 and the XOR function based on the two previous steps of evolution. The resulting histograms of the distribution of brightness for each color of the encrypted image confirm the high quality of encryption based on the proposed method.

Formation of streams of binary sequences with controlled structure of "cellular" automata in homogeneous register environments

Objective. Development of a method for organizing the process of forming flows register structure, patented by the author at the Department of DSTU, which is a cellular automaton of binary sequences with a controlled structure of "cellular" automata in homogeneous register environments. Method. To solve the set system problem, a process model was built in order to determine the factors that allow changing the sequence of flow elements. Result. When studying the most common generators of pseudo-random streams based on linear register media with modulo two adders in feedback circuits, which are "cellular" automata, it was established from the tables of environment states that the factors determining the structure of the generated streams of binary sequences are the sequence of states , are the initial state of the register of a homogeneous medium and the feedback structure determined by the transition function of the cellular automaton. Conclusion. It is shown that by varying the initial state of the cellular automaton and the structure of feedbacks as control tools, it seems possible to form binary pseudo-random streams of states with different structures, different order of flow elements, bringing their characteristics closer to random ones. Examples of the implementation of the flow structure control process are given, confirming this assumption. A typical structure of a stream shaper with a managed structure based on a homogeneous one is given.

MUSE: Multimodal Separators for Efficient Route Planning in Transportation Networks

Many algorithms compute shortest-path queries in mere microseconds on continental-scale networks. Most solutions are, however, tailored to either road or public transit networks in isolation. To fully exploit the transportation infrastructure, multimodal algorithms are sought to compute shortest paths combining various modes of transportation. Nonetheless, current solutions still lack performance to efficiently handle interactive queries under realistic network conditions where traffic jams, public transit cancelations, or delays often occur. We present a multimodal separators–based algorithm (MUSE), a new multimodal algorithm based on graph separators to compute shortest travel time paths. It partitions the network into independent, smaller regions, enabling fast and scalable preprocessing. The partition is common to all modes and independent of traffic conditions so that the preprocessing is only executed once. MUSE relies on a state automaton that describes the sequence of modes to constrain the shortest path during the preprocessing and the online phase. The support of new sequences of mobility modes only requires the preprocessing of the cliques, independently for each partition. We also augment our algorithm with heuristics during the query phase to achieve further speedups with minimal effect on correctness. We provide experimental results on France’s multimodal network containing the pedestrian, road, bicycle, and public transit networks.

Энергосберегающее кодирование частичных состояний параллельного автомата

The problem of a low-power assignment of the partial states of a parallel automaton is considered. A method to solve that problem is suggested that provides minimizing the number of memory elements in the implementing circuit of the automaton and minimization of their switching activity. The problem is reduced to finding a minimal weighted cover of a graph with its complete bipartite sub-graphs (bi-cliques).

A multiplicity of statistical models for modeling the degeneracy of living communicating holons

Communicating living systems detect and process a multiplicity of events with degeneracy, to continuously cope with environmental aleatoric incertitude. The concept of holon, communicating at various scales of living organizations, is hereafter formalized through dynamical systems driven by the multiplicity of statistical models. Then, the stimulus-response of elementary biological holons can be modeled by memoryless Boolean automata with different signal processing methods, in presence of noise and stochastic interference. Detection of a specified signal, to update the automaton state, can be performed via multiple families of update functions, with differentiated balances between sensitivity and specificity in presence of interference: (i) Neyman-Pearson update functions provide the best possible sensitivity to detect the signal of interest in absence of interference, but cannot guarantee a desired specificity; (ii) by detecting large amplitudes of any signal in noise, update functions based on Random Distortion Testing yield a suboptimal sensitivity to detect the signal in noise, but guarantee a wanted specificity even in presence of interference. Thus, statistical inference theories offer functional and structural redundancy and open prospects to model fractal-like holarchies, via networks of communicating degenerated automata, to feature properties of the immune system.

Adaptive personalized recommender system using learning automata and items clustering

The personalized recommender systems provide user-related services based on user preferences; these preferences are recorded in an individual profile. Therefore, the more complete and precise each user profile leads more successful the recommendation process. The people’s interests change over time though traditional researches do not follow these changes regularly. Under such circumstances, designing an efficient user model to track users’ interests is greatly important. In the current study, we suggest an algorithm to create the learning automata-based user profiling. Due to many items and the commonality of features between them, we clustered items. In this technique, a learning automaton is assigned to the active user. The learning automaton adjusts the amount of user interest in each cluster based on user feedback. As the user interactions with the system increase, the internal state of the learning automaton converges towards the user’s genuine interests in the item clusters. The experimental results demonstrate that our algorithm outperforms compared approaches in precision, recall, RMSE, and MAE. In addition, the proposed algorithm for new users has acceptable performance.

Efficient Automaton Theoretical Vacuity Detection for Formal Properties

Model checking is a powerful technique for verifying the correctness of systems with respect to the requirements. While some errors happen in the property, the model itself, or the environment, we think that satisfaction of the property is meaningless (vacuous) satisfaction. It misleads users of model-checking that a system is correct. Traditional temporal logic vacuity detection is based on a syntactic definition. It is undesirable because vacuity detection would depend on syntactic formalization choices that have no effect on the semantics. This article presents an automaton-based semantic vacuity detection method which synthesizes the property into the automaton and detects the vacuity by detecting the reachability of the automaton state. Compared with the traditional syntactic-based vacuity detection, the proposed method is well suited for detecting vacuity with respect to multiple occurrences of a sub-formula. At the same time, we do not distinguish the temporal logic language. As long as the property can be synthesized into an automaton, this method can be well applied. We extend the vacuity to the satisfaction of real-time properties. The real experiments show that this method is applied efficiently in practical vacuity detection. To our knowledge, it is the first attempt to present and solve practical vacuity in an automaton view.

Using the Context-Sensitive Policy Mechanism for Building Data Acquisition Systems in Large Scale Distributed Cyber-Physical Systems Built on Fog Computing Platforms

The article deals with the use of context-sensitive policies in the building of data acquisition systems in large scale distributed cyber-physical systems built on fog computing platforms. It is pointed out that the distinctive features of modern cyber-physical systems are their high complexity and constantly changing structure and behavior, which complicates the data acquisition procedure. To solve this problem, it is proposed to use an approach according to which the data acquisition procedure is divided into two phases: model construction and data acquisition, which allows parallel realization of these procedures. A distinctive feature of the developed approach is that the models are built in runtime automatically. As a top-level model, a multi-level relative finite state operational automaton is used. The automaton state is described using a multi-level structural-behavioral model, which is a superposition of four graphs: the workflow graph, the data flow graph, the request flow graph and the resource graph. To implement the data acquisition procedure using the model, the context-sensitive policy mechanism is used. The article discusses possible approaches to implementation of suggested mechanisms and describes an example of application.

Efficient Construction of the Equation Automaton

This paper describes a fast algorithm for constructing directly the equation automaton from the well-known Thompson automaton associated with a regular expression. Allauzen and Mohri have presented a unified construction of small automata and gave a construction of the equation automaton with time and space complexity in O(mlogm+m2), where m denotes the number of Thompson automaton transitions. It is based on two classical automata operations, namely epsilon-removal and Hopcroft’s algorithm for deterministic Finite Automata (DFA) minimization. Using the notion of c-continuation, Ziadi et al. presented a fast computation of the equation automaton in O(m2) time complexity. In this paper, we design an output-sensitive algorithm combining advantages of the previous algorithms and show that its computational complexity can be reduced to O(m×|Q≡e|), where |Q≡e| denotes the number of states of the equation automaton, by an epsilon-removal and Bubenzer minimization algorithm of an Acyclic Deterministic Finite Automata (ADFA).

A cellular-automata model for assessing the sensitivity of the street network to natural terrain

ABSTRACT Natural and human-made features are not exclusive in settlements but interact across time and space, placing the context in constant evolution. The purpose of this paper is to search for the influence of terrain, a natural feature, on the configuration of the street network, a human-made feature, by analysing the results of two transition states of cellular automata used to model street networks. This work uses data from open-source projects and open-source applications. The first transition state models the street network considering the neighbourhood rules and randomness, assuming the natural terrain and street are exclusive. The second transition state models the street network as the product of characteristics of the terrain, neighbourhood rules, and randomness, thus assuming the natural terrain and street network interacting with one another. The model is run thirteen times for four different cities by varying the terrain characteristics and calibrated by comparing the simulated street maps with recent street maps. The results are compared and found that the CA model with the second transition state yields better simulation results than the first transition state. In one of the four cities studied, the first transition state results are similar to a specific state of the second transition state, indicating a weak inter-connectedness between the terrain and the street network in the mega-city. Further research can reveal whether the amount of inter-connectedness is specific to the city’s terrain or size. The recognition of the inter-connectedness of the road to terrain can help plan for resilient human settlements.

Identification of Long-Term Behavior of Natural Circulation Loops: A Thresholdless Approach from an Initial Response

Natural circulation loop (NCL) systems are buoyancy-driven heat exchangers that are used in various industrial applications. The concept of passive heat exchange in NCL systems is attractive, because there is no need for an externally driven equipment (e.g., a pump) to maintain the fluid circulation. However, relying on buoyancy as the sole driving force may lead to several potential difficulties, one of which is generation of (possibly) time-varying nonlinearities in the dynamical system, where a difference in the time scales of heat transfer and fluid flow causes the flow to change from a steady-state regime to either an oscillatory regime or a flow-reversal regime, both of which are undesirable. In this paper, an algorithm is developed using tools of symbolic time-series analysis (e.g., probabilistic finite state automata (PFSA)) for the purpose of identifying selected regimes of operation in NCL systems using only data from the early transient operation, where the underlying principle is built upon the concept of pattern classification from measurements of fluid-flow dynamics. The proposed method is shown to be capable of identifying the current regime of operation from the initial time response under a given set of operational parameters. The efficacy of regime classification is demonstrated by testing on two datasets, generated from numerical simulation of a MATLAB SimuLink model that has previously been validated with experimental data. The results of the proposed PFSA-based classification are compared with those of a hidden Markov model (HMM) that serves as the baseline.