Modal Automata Research Articles

Hardware implementation of Boolean functions based on the automaton model

Objectives. Currently, electronic control devices are increasingly being introduced into various household and production products. Microcontrollers of a wide variety of configurations are widely used as such devices. Another approach can be proposed where a control device with a standard structure is synthesized from typical integrated circuits and implements a Boolean function describing the required control actions.The purpose of the work is to investigate the possibility of implementing Boolean functions using devices with a standard structure, the design of which is based on the use of a discrete automaton model.Methods. The original Boolean function to be implemented is given as a disjunctive normal form. A binary decision diagram (BDD) is built for such function, optimized by the number of vertices, on the basis of which a graph of transitions of a synchronous Moore automaton with an abstract state is formed. Further, after performing the state encoding step of the machine, input information for flashing (programming) of the matrix memory of the read-only memory (ROM) is generated based on its transition table.Results. A device that implements a Boolean function based on an automaton model is synthesized from typical microcircuits. The main component is ROM, which, according to the standard structure of the device, is supplemented by a shift register, a state register, a trigger and three selectors of the initial and two final states.Conclusion. The process of designing a device with standard structure that implements the Boolean function, as a result, comes down to programming the ROM matrix memory based on an automaton transition table. The use of a reprogrammable ROM allows to change the functionality of the device while maintaining the previous circuit implementation. The disadvantage of such a device, as well as devices implemented on the basis of microcontrollers, is the low speed, the advantage is the possibility of use it in various products and devices, primarily for household purposes, which do not require a high-speed response to the change of input signal.

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.

Multi-Agent Tree Search with Dynamic Reward Shaping

Sparse rewards and their representation in multi-agent domains remains a challenge for the development of multi-agent planning systems. While techniques from formal methods can be adopted to represent the underlying planning objectives, their use in facilitating and accelerating learning has witnessed limited attention in multi-agent settings. Reward shaping methods that leverage such formal representations in single-agent settings are typically static in the sense that the artificial rewards remain the same throughout the entire learning process. In contrast, we investigate the use of such formal objective representations to define novel reward shaping functions that capture the learned experience of the agents. More specifically, we leverage the automaton representation of the underlying team objectives in mixed cooperative-competitive domains such that each automaton transition is assigned an expected value proportional to the frequency with which it was observed in successful trajectories of past behavior. This form of dynamic reward shaping is proposed within a multi-agent tree search architecture wherein agents can simultaneously reason about the future behavior of other agents as well as their own future behavior.

A framework for modelling spatio-temporal informal settlement growth prediction

Many developing countries grapple with the problem of rapid informal settlement emergence and expansion. This exacts considerable costs from neighbouring urban areas, largely as a result of environmental, sustainability and health-related problems associated with such settlements, which can threaten the local economy. Hence, there is a need to understand the nature of, and to be able to predict, future informal settlement emergence locations as well as the rate and extent of such settlement expansion in developing countries.A novel generic framework is proposed in this paper for machine learning-inspired prediction of future spatio-temporal informal settlement population growth. This data-driven framework comprises three functional components which facilitate informal settlement emergence and growth modelling within an area under investigation. The framework outputs are based on a computed set of influential spatial feature predictors pertaining to the area in question. The objective of the framework is ultimately to identify those spatial and other factors that influence the location, formation and growth rate of an informal settlement most significantly, by applying a machine learning modelling approach to multiple data sets related to the households and spatial attributes associated with informal settlements. Based on the aforementioned influential spatial features, a cellular automaton transition rule is developed, enabling the spatio-temporal modelling of the rate and extent of future formations and expansions of informal settlements.

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).

Dynamic Automaton-Guided Reward Shaping for Monte Carlo Tree Search

Reinforcement learning and planning have been revolutionized in recent years, due in part to the mass adoption of deep convolutional neural networks and the resurgence of powerful methods to refine decision-making policies. However, the problem of sparse reward signals and their representation remains pervasive in many domains. While various rewardshaping mechanisms and imitation learning approaches have been proposed to mitigate this problem, the use of humanaided artificial rewards introduces human error, sub-optimal behavior, and a greater propensity for reward hacking. In this paper, we mitigate this by representing objectives as automata in order to define novel reward shaping functions over this structured representation. In doing so, we address the sparse rewards problem within a novel implementation of Monte Carlo Tree Search (MCTS) by proposing a reward shaping function which is updated dynamically to capture statistics on the utility of each automaton transition as it pertains to satisfying the goal of the agent. We further demonstrate that such automaton-guided reward shaping can be utilized to facilitate transfer learning between different environments when the objective is the same.

Representing stand-alone automata by characteristic polynomials over a finite field

This paper proposes a method of representing a deterministic stand-alone output automaton by a minimal characteristic polynomial over a finite field. It is shown that defining various automaton transition and output functions allows using the algorithm developed to build the sets of minimal polynomials, different in their powers. Estimates of the relevant sets are given here. We have identified the relation between a characteristic minimal polynomial and an ergodic stochastic matrix defining the sequence developed by a stand-alone automaton. It is shown that the minimal degree of a characteristic polynomial depends linearly on the power of the automaton state set and on the accuracy of representing the elements of a given limiting vector of a stochastic matrix.

On stabilization of an automaton model of migration processes

AbstractA dynamic system of cities with migrants is considered. The wage function is each city depends on the number of migrants in the city. The system is modeled by an automaton whose state is the vector consisting of the numbers of migrants in the cities. The transition function of the automaton reflects the conditions for transfers of migrants between cities. The system stabilizes if the moves are stopped at some point. We find conditions for stabilization of such system depending on the restrictions on the wage function and the automaton transition function. It is shown that if the functions of wages are strictly decreasing, if their ranges are disjoint, and if the transition function is defined so that a migrant moves to another city if and only if its salary increases, then the system necessarily stabilizes and its final state depends only on the total number of migrants and does not depend on their initial distribution over the cities. However, if the transition function is changed so that a migrant moves also if its salary is preserved, but the total wages in all cities are increased, then a monotonous decrease in the wage functions is sufficient for stabilization of the system.

A New Supervisor Synthesis Approach for Discrete-Event Systems With Infinite Behavior

w-closure (together with w-controllability) plays an important role in the supervisor synthesis for liveness specifications imposed on discrete-event systems (DESs) with infinite behavior. However, it is not closed under arbitrary unions, and thus there does not exist the supremal w-closed (and w-controllable) sublanguage. In this paper, we first develop an algorithm to compute a subautomaton of the automaton representing an arbitrarily given w-language by deleting all bad loops (which lead to un-closedness of the given language) in the automaton, and show that the obtained subautomaton represents an w-closed sublanguage and is maximal from the perspective of an automaton transition graph. With this algorithm, we propose a new approach to construct a supervisor synthesizing an w-language even if it is not w-closed. Furthermore, we prove that, compared with the supervisor computed by the Thistle's supervisor synthesis approach, the supervisor synthesized by our approach is often more permissive. Examples are presented for illustration.

Completeness for the modal μ-calculus: Separating the combinatorics from the dynamics

The modal mu-calculus is a very expressive formalism extending basic modal logic with least and greatest fixpoint operators. In the seminal paper introducing the formalism in the shape known today, Kozen also proposed an elegant axiom system, and he proved a partial completeness result with respect to the Kripke-style semantics of the logic. The problem of proving Kozen's axiom system complete for the full language remained open for about a decade, until it was finally resolved by Walukiewicz. In this paper we develop a framework that will let us clarify and simplify parts of Walukiewicz' proof.Our main contribution is to take the automata-theoretic viewpoint, already implicit in Walukiewicz' proof, much more seriously by bringing automata explicitly into the proof theory. Thus we further develop the theory of modal parity automata as a mathematical framework for proving results about the modal mu-calculus. Once the connection between automata and derivations is in place, large parts of the completeness proof can be reformulated as purely automata-theoretic theorems. From a conceptual viewpoint, our automata-theoretic approach lets us distinguish two key aspects of the mu-calculus: the one-step dynamics encoded by the modal operators, and the combinatorics involved in dealing with nested fixpoints. This “deconstruction” allows us to work with these two features in a largely independent manner.More in detail, prominent roles in our proof are played by two classes of modal automata: next to the disjunctive automata that are known from the work of Janin & Walukiewicz, we introduce here the class of semi-disjunctive automata that roughly correspond to the fragment of the mu-calculus for which Kozen proved completeness. We will establish a connection between the proof theory of Kozen's system, and two kinds of games involving modal automata: a satisfiability game involving a single modal automaton, and a consequence game relating two such automata. In the key observations on these games we bring the dynamics and combinatorics of parity automata together again, by proving some results that witness the nice behaviour of disjunctive and semi-disjunctive automata in these games. As our main result we prove that every formula of the modal mu-calculus provably implies the translation of a disjunctive automaton; from this the completeness of Kozen's axiomatization is immediate.

Language-Theoretic and Finite Relation Models for the (Full) Lambek Calculus

We prove completeness for some language-theoretic models of the full Lambek calculus and its various fragments. First we consider syntactic concepts and syntactic concepts over regular languages, which provide a complete semantics for the full Lambek calculus $${\mathbf {FL}}_\perp $$FLź. We present a new semantics we call automata-theoretic, which combines languages and relations via closure operators which are based on automaton transitions. We establish the completeness of this semantics for the full Lambek calculus via an isomorphism theorem for the syntactic concepts lattice of a language and a construction for the universal automaton recognizing the same language. Finally, we use automata-theoretic semantics to prove completeness of relation models of binary relations and finite relation models for the Lambek calculus without and with empty antecedents (henceforth: $$\mathbf L $$L and $$\mathbf L1 $$L1), thus solving a problem left open by Pentus (Ann Pure Appl Log 75:179---213, 1995).

Developing a software system for automata-based code generation

This paper is devoted to the development of the State Machine Generator system meant for automatic code generation based on the principles of automata-based programming. This system models program logic in terms of the finite-state automaton transition graph and generates program code on its basis. Basic functions of the developed software system and the mechanism of their implementation are described. This paper also proposes a new pattern for designing automaton programs. As an example, State Machine Generator is used to develop a bug tracker system for software testing.

Local structure approximation as a predictor of second-order phase transitions in asynchronous cellular automata

The mathematical analysis of the second-order phase transitions that occur in ?-asynchronous cellular automata field is a highly challenging task. From the experimental side, these phenomena appear as a qualitative change of behaviour which separates a behaviour with an active phase, where the system evolves in a stationary state with fluctuations, from a passive state, where the system is absorbed in a homogeneous fixed state. The transition between the two phases is abrupt: we ask how to analyse this change and how to predict the critical value of the synchrony rate ?. We show that an extension of the mean-field approximation, called the local structure theory, can be used to predict the existence of second-order phase transitions belonging to the directed percolation university class. The change of behaviour is related to the existence of a transcritical bifurcation in the local structure maps. We show that for a proper setting of the approximation, the form of the transition is predicted correctly and, more importantly, an increase in the level of local structure approximation allows one to gain precision on the value of the critical synchrony rate which separates the two phases.

INTERMEDIATE ALGEBRA OF TRANSITIONS IN MICROPROGRAM FINAL-STATE MACHINE

The problem of formalization of representation of final-state machine, where the part of automaton transition is realized in noncanonicalway, is solved. A new approach for organization of the function of transitions of the final-state machine is proposed. According toit the function of transitions is represented as a family of partial functions, each of which is defined only on the part of the domain of thefunction of transitions, and corresponds to a subset of the automaton transitions. According to the proposed approach the traditional representation of the final-state machine as a polybasic algebra is changed. First, the mutual independence of the function of transitions and function of outputs that form the signature of algebra, allows us to consider them separately from each other. This way leads to presentation of the final-state machine as two algebras: the algebra of transitions whose signature contains only the function of transitions and algebra of outputs whose signature contains only the function of outputs. Second, the representation of the function of transitions in the form of a set of partial functions leads to the replacement of the algebra of transitions by the set of subalgebras of transitions, a signature of each of which is formed by partial function of transitions.The example of the final-state machine with a counter shows that the law of transformation of codes of states within a certain subset oftransitions can be set by an algebraic function (operation of transitions) using scalar interpretation of codes of states of the structural finalstatemachine. The representation of scalar interpretation of codes of states and the operation of transitions as so-called intermediate algebraof transitions isomorphic to both according subalgebras of transitions of the abstract and equivalent structural final-state machines is proposed.

There exist one-dimensional transitive cellular automata with non-empty set of strictly temporally periodic points

In a Cantor metric space B Z , we present a one-sided cellular automaton which positively answers the question Does it exist a transitive cellular automaton (B Z , F) with non-empty set of strictly temporally periodic points? The question can be found in a current and recognized literature of the subject.

English

This paper models and supervises kernel railroad crossing (KRC) systems using timed Petri nets and focuses on the control synthesis method, which consists in computing new firing conditions for the timed automaton (TA) transitions so that the forbidden locations are no longer reachable. The system to be modeled and supervised using timed Petri nets is converted to a TA and is analyzed using automata so that the functioning of the system respects given specifications. The main reason of using automata is that although the timed Petri nets supervisor controls the system, it fails to define the time units needed for the undefined time of a transition. Simulation results show the soundness of KRC modeling and supervision in the sense of ensuring the safety and maximizing utility (the gate should be opened as long as possible).

Modal Specifications for Probabilistic Timed Systems

Modal automata are a classic formal model for component-based systems that comes equipped with a rich specification theory supporting abstraction, refinement and compositional reasoning. In recent years, quantitative variants of modal automata were introduced for specifying and reasoning about component-based designs for embedded and mobile systems. These respectively generalize modal specification theories for timed and probabilistic systems. In this paper, we define a modal specification language for combined probabilistic timed systems, called abstract probabilistic timed automata, which generalizes existing formalisms. We introduce appropriate syntactic and semantic refinement notions and discuss consistency of our specification language, also with respect to time-divergence. We identify a subclass of our models for which we define the fundamental operations for abstraction, conjunction and parallel composition, and show several compositionality results.

Topology-induced phase transitions in totalistic cellular automata

Notwithstanding numerous papers are dedicated to the intriguing dynamics of cellular automata (CAs), which are mathematical models in which the time, space and state domain are discrete, in most of them the discussion is confined to the sensitivity of a CA’s dynamical properties to the imposed initial conditions. Since the dynamics of a CA relies on both the states of its spatial entities and the interconnections between them, to which we refer as a CA’s topology, it is striking that the influence of the latter on the evolved dynamics has received only minor attention. To fill this gap, we investigate in this paper how a CA’s topology affects its dynamical properties by relying on Lyapunov exponents. We demonstrate the existence of so-called topology-induced phase transitions and topological bifurcation points, which lead us to discriminate between intrinsically complex CAs, on the one hand, and topology-mediated complex CAs on the other hand.

Automata for the verification of monadic second-order graph properties

The model-checking problem for monadic second-order logic on graphs is fixed-parameter tractable with respect to tree-width and clique-width. The proof constructs finite automata from monadic second-order sentences. These automata recognize the terms over fixed finite signatures that define graphs satisfying the given sentences. However, this construction produces automata of hyper-exponential sizes, and is thus impossible to use in practice in many cases. To overcome this difficulty, we propose to specify the transitions of automata by programs instead of tables. Such automata are called fly-automata. By using them, we can check certain monadic second-order graph properties with limited quantifier alternation depth, that are nevertheless interesting for Graph Theory. We give explicit constructions of automata relative to graphs of bounded clique-width, and we report on experiments.

A Learning System for a Computational Science Related Topic

Computational science is an interdisciplinary field in which mathematical models combined with scientific computing methods are used to study systems of real-world problems. One of such mathematical models is automata theory. This paper introduces a learning system for automata theory. The learning system is a combination of java and robots technologies. Learners can build their own automaton graphically in the systems’ interface, and then pass it to the robot, which can then simulate the automaton transitions. Learners can learn by observing the robot's motion. A preliminary evaluation shows the effectiveness of the system in classroom.