Moore Machines Research Articles

A Calculus for the Specification, Design, and Verification of Distributed Concurrent Systems

A calculus for the specification and verification of distributed concurrent interactive real time systems is introduced. Systems are specified by their interface behavior formalized by interface predicates and interface assertions. System designs in terms of architectures of distributed networks of interactive systems are constructed by concurrent composition of subsystems. The specification of system designs is calculated from the specifications of their subsystems. Verification is done by proof rules which are based on the concepts of causality and realizability justified by the operational model in terms of generalized Moore machines, Moore machines not restricted to finite state spaces. The calculus supports interface specification and reasoning both about untimed as well as timed distributed concurrent systems. This includes the design of cyber-physical systems. Real-time is used, in particular, to specify time sensitive behavior and to prove properties related to causality and realizability, properties which hold for all Moore machines. On this basis, a calculus is worked out and illustrated by small examples. The calculus is shown to be sound and relatively complete.

Specification and verification of concurrent systems by causality and realizability

A logical theory for interface specification and verification of distributed, concurrent, interactive, real-time systems is worked out based on a semantic foundation including operational and denotational semantics. It supports a calculus for the specification and verification of concurrent interactive systems by interface assertions. Systems are composed acting concurrently and interacting via streams exchanged over their channels forming feedback loops. A denotational semantics is defined handling feedback communication by recursion and fixpoints based on strong causality and realizability instead of monotonicity. The resulting verification calculus for the specification logic is proved to be sound and relatively complete with respect to an operational semantics in terms of generalized Moore machines. Actually, two models of concurrent systems are defined, a more abstract one with communication and interaction modeled by untimed streams and a more concrete one working with timed streams. The untimed model is an abstraction of the timed model. The timed model allows expressing the laws of causality and realizability. Moreover, the timed model can be used to specify real-time properties.

Moore machines duality

We present a simple algorithm to find the Moore machine with the minimum number of states equivalent to a given one.

Learners' Languages

In "Backprop as functor", the authors show that the fundamental elements of deep learning -- gradient descent and backpropagation -- can be conceptualized as a strong monoidal functor Para(Euc)$\to$Learn from the category of parameterized Euclidean spaces to that of learners, a category developed explicitly to capture parameter update and backpropagation. It was soon realized that there is an isomorphism Learn$\cong$Para(Slens), where Slens is the symmetric monoidal category of simple lenses as used in functional programming. In this note, we observe that Slens is a full subcategory of Poly, the category of polynomial functors in one variable, via the functor $A\mapsto Ay^A$. Using the fact that (Poly,$\otimes$) is monoidal closed, we show that a map $A\to B$ in Para(Slens) has a natural interpretation in terms of dynamical systems (more precisely, generalized Moore machines) whose interface is the internal-hom type $[Ay^A,By^B]$. Finally, we review the fact that the category p-Coalg of dynamical systems on any $p \in$ Poly forms a topos, and consider the logical propositions that can be stated in its internal language. We give gradient descent as an example, and we conclude by discussing some directions for future work.

МОДЕЛИРОВАНИЕ ДИСКРЕТНЫХ СИСТЕМ УПРАВЛЕНИЯ НА ОСНОВЕ АВТОМАТОВ МИЛИ И МУРА В САПР PROTEUS 8

In the course of the works, discrete control systems based on Mealy and Moore machines in Proteus 8 CAD have been designed and modeled. The author analyzes functional capabilities of the VSM (virtual simulation environment) of the Proteus Design Suite virtual modeling environment by Labcenter Electronics. Its application is considered to be useful for developing models and testing discrete systems.

Automation of quantum Braitenberg vehicles using finite automata: Moore machines

Since the advent of quantum computation, there have been attempts to apply quantum mechanics to robotics and develop quantum robots. In this paper, we discuss the working of classical Braitenberg vehicles and the various problems which lead us to propose a novel improvement by automating it using classical finite automata, Moore machines. We then improve by introducing an intrinsic nature to it such that it stops its motion without requiring external signals, by using entanglement. This leads to our design of a quantum automated Braitenberg vehicle which we improve by incorporating the possibility of external control over its movement. We implement the circuits in IBM quantum experience and obtain results matching our theoretical predictions. This paper makes the following contributions: an experimental verification of the quantum logic with reasonably good results despite decoherence and errors in quantum gate applications, the idea of introducing intrinsic behaviour using quantum mechanics, the idea of flexibility in developing manual external controls, and achieving better results than classical robots using lesser number of gates.

Learning Moore machines from input–output traces

The problem of learning automata from example traces (but no equivalence or membership queries) is fundamental in automata learning theory and practice. In this paper, we study this problem for finite-state machines with inputs and outputs, and in particular for Moore machines. We develop three algorithms for solving this problem: (1) the PTAP algorithm, which transforms a set of input–output traces into an incomplete Moore machine and then completes the machine with self-loops; (2) the PRPNI algorithm, which uses the well-known RPNI algorithm for automata learning to learn a product of automata encoding a Moore machine; and (3) the MooreMI algorithm, which directly learns a Moore machine using PTAP extended with state merging. We prove that MooreMI has the fundamental identification in the limit property. We compare the algorithms experimentally in terms of the size of the learned machine and several notions of accuracy, introduced in this paper. We also carry out a performance comparison against two existing tools (LearnLib and flexfringe). Finally, we compare with OSTIA, an algorithm that learns a more general class of transducers and find that OSTIA generally does not learn a Moore machine, even when fed with a characteristic sample.

Системний підхід до аналізу процесу функціонування закладу вищої освіти

It is shown that the study of the processes of the functioning of institutions of higher education and the publication of the results of these studies in scientific journals are mainly aimed at identifying the dependencies of the quality of training specialists in these institutions on one or more coordinates of this process in the conditions of ignoring the influence of many other its coordinates, and in the vast majority without taking into account their changes in time, that is, using mathematical models of these dependencies in the space of Moore's machines, while adequate representation of the processes of functioning of the institutions Higher education is possible only in the space of Mill's machines. It is proposed to use the system approach as an ideology and system analysis as a method for studying the processes of functioning of institutions of higher education and to determine all the components of these processes in the first two stages of the application of the method, as a result of which the institution of higher education identified as an object of research on the environment and formed all points , in which this object of research carries out contacts with the environment, and specifies all 15 environmental impacts on the object of research and all 12 effects of the object and research into the environment. It is shown that in order for mathematical models of the processes of functioning of higher education institutions to represent these processes in the space of Mill's machines, they must be synthesized using dependencies in which all variables are functions of time in its continuous or discrete interpretations. As criteria for evaluating the results, it is proposed to use such integral criteria as the image of the institution of higher education and the costs necessary to ensure its functioning, the first of which — the image — requires maximization with constraints on costs, and the second — the cost — requires minimization with restrictions on the image, that is, when solving the problem with their use, the strategy may be either maximizing, or minimax, and the optimum point is saddle.

Moore-Machine Filtering for Timed and Untimed Pattern Matching

Monitoring is an important body of techniques in runtime verification of real-time, embedded, and cyber-physical systems. Mathematically, the monitoring problem can be formalized as a pattern matching problem against a pattern automaton. Motivated by the needs in embedded applications---especially the limited channel capacity between a sensor unit and a processor that monitors---we pursue the idea of filtering as preprocessing for monitoring. Technically, for a given pattern automaton, we present a construction of a Moore machine that works as a filter. The construction is automata-theoretic, and we find the use of Moore machines particularly suited for embedded applications, not only because their sequential operation is relatively cheap but also because they are amenable to hardware acceleration by dedicated circuits. We prove soundness (i.e., absence of lost matches), too. We work in two settings: in the untimed one, a pattern is an NFA; in the timed one, a pattern is a timed automaton. The extension of our untimed construction to the timed setting is technically involved, but our experiments demonstrate its practical benefits.

Эффективные модели и схемы цифровых устройств циклического действия

The work considersmodels and schemes of widespread digital devices of cyclic action. They includecoders and decoders of information transfer system, control units of processors, generators of codes, counters, distributors of impulses etc. Three models of devices for consecutive, parallel and ripple through information transfer are suggested and proved. The structure of the models is presented by a set of blocks with original operation algorithms and connections between their blocks. The blocks are implemented in the form of Moore machines (in case of consecutive transfer) and Mealy machines (in case of parallel and ripple through transfer). A technique for synthesizing devices based on these models with the use of canonic synthesis methods and ofHuffman transition tablesmodified by the authoris suggested. This allows implementing compactly devices of practically any complexity. Algorithms for transition from models with ripple through transfer to models with parallel and consecutive transfer are described. Examples of implementing models in the form of concrete schemes confirming their efficiency are considered.

Realization of information technology of character recognition based on competing cellular automata

We examined the possibility of applying cellular automata to solve the problem on recognition of text characters. For this purpose, we introduced the notion of competing cellular automata and developed algorithms of their functioning and interaction. In order to implement the proposed algorithms, we created modeling software. It allowed us to evaluate effectiveness of the cellular-automaton algorithms to conduct experiments on text character recognition using the English alphabet and to demonstrate a number of advantages in comparison with other methods. We investigated a description of the solution to the problem on selecting the structural attributes in the images of text characters, which directly affect the quality of recognition. In the present work, it is proposed to use a set of cellular automata constructed on the diagrams of states of Moore and Mealy machines for each type of cellular automata, to determine the end points, junctions and cycles in characters. We considered operation of the modeling program. The advantages of the given technology are the simplicity of rules of interaction, easy parallelization of the process of recognition, the possibility of recognition of distorted and partially overlapping characters. We compared performance quality and efficiency of the commercially available system ABBYY FineReader, which has demonstrated high performance indicators of the developed recognition technology

Generalized Boolean logic Driven Markov Processes: A powerful modeling framework for Model-Based Safety Analysis of dynamic repairable and reconfigurable systems

This paper presents a modeling framework that permits to describe in an integrated manner the structure of the critical system to analyze, by using an enriched fault tree, the dysfunctional behavior of its components, by means of Markov processes, and the reconfiguration strategies that have been planned to ensure safety and availability, with Moore machines. This framework has been developed from BDMP (Boolean logic Driven Markov Processes), a previous framework for dynamic repairable systems. First, the contribution is motivated by pinpointing the limitations of BDMP to model complex reconfiguration strategies and the failures of the control of these strategies. The syntax and semantics of GBDMP (Generalized Boolean logic Driven Markov Processes) are then formally defined; in particular, an algorithm to analyze the dynamic behavior of a GBDMP model is developed. The modeling capabilities of this framework are illustrated on three representative examples. Last, qualitative and quantitative analysis of GDBMP models highlight the benefits of the approach.

Globally asynchronous systems of interactive Moore state machines

The problem of organising the temporal behaviour of globally asynchronous systems consisting of parallel interacting blocks is discussed. System blocks are represented by the Moore state machine model. The earlier suggested GALA (Globally Asynchronous, Locally Arbitrary) design methodology is used. This methodology is based on decomposing the system to a Processors Stratum (stratum of blocks) and a Synchronisation Stratum (synch-stratum). The synch-stratum acts as a distributed asynchronous clock network that produces local synch-signals for the processor stratum, which basically can be a synchronous prototype. The synch-stratum is a self-timed circuit that interacts with the processor stratum (system devices) via the handshake protocol. Every local device that has received the request signal from the synch-stratum produces the acknowledgment signal and sends it back. In this study, some logic circuits of universal modules are suggested. They provide an easy way to design any synch-stratum for parallel synchronisation of system blocks with arbitrary interconnection graphs and for wave synchronisation of system blocks with acyclic interconnection graph.

Flight Safety Assessment and Management for Takeoff Using Deterministic Moore Machines

This paper presents a novel flight safety assessment and management augmentation to the flight management system designed to assist a flight crew in avoiding or recovering from impending loss-of-control situations. Nominally, this system serves as a passive monitor but, in high-risk situations, warnings and (ultimately) override actions are initiated to mitigate the high-risk situation. In this work, flight safety assessment and management is applied to the task of preserving safety during takeoff, which is one of the highest-risk phases of flight. Flight safety assessment and management is specified as a deterministic Moore machine that can ultimately be certified using existing software certification processes. To facilitate understanding and to reduce state-space complexity, flight safety assessment and management’s state machines are split into longitudinal and lateral-directional submachines that identify and mitigate loss-of-control contributing factors associated with aircraft dynamics and control constraints. Case studies based on documented takeoff accidents are presented to evaluate flight safety assessment and management’s ability to maintain safe flight in realistic loss-of-control scenarios. Results from these case studies illustrate that flight safety assessment and management could have averted the takeoff accidents that were considered. A discussion of other factors that must be considered before realizing a comprehensive flight safety assessment and management capability for takeoff is provided.

Implementation of finite-state machines based on programmable logic ICs with the help of the merged model of Mealy and Moore machines

The problem concerning the synthesis of finite-state machines (FSMs) based on programmable logic ICs, in which FSM’s output variables serve as the code (or part of the code) of internal states, has been examined. A solution to the problem is obtained with the help of the merged model of Mealy and Moore machines. A principal distinction between the proposed and well-known techniques is that an initial FSM undergoes no conversions related to an increase in the number of internal states and transitions thereof. The necessary conditions under which output variables can be used as the code of FSM’s internal states are presented. The method for synthesizing the merged model AC of Mealy and Moore machines is described. Basic results of investigations, as well as promising directions of further studies concerned with the development of new structural models of FSMs, are discussed.

Quantitative Kleene coalgebras

We present a systematic way to generate (1) languages of (generalised) regular expressions, and (2) sound and complete axiomatizations thereof, for a wide variety of quantitative systems. Our quantitative systems include weighted versions of automata and transition systems, in which transitions are assigned a value in a monoid that represents cost, duration, probability, etc. Such systems are represented as coalgebras and (1) and (2) above are derived in a modular fashion from the underlying (functor) type of these coalgebras. In previous work, we applied a similar approach to a class of systems (without weights) that generalizes both the results of Kleene (on rational languages and DFA’s) and Milner (on regular behaviours and finite LTS’s), and includes many other systems such as Mealy and Moore machines. In the present paper, we extend this framework to deal with quantitative systems. As a consequence, our results now include languages and axiomatizations, both existing and new ones, for many different kinds of probabilistic systems.

Non-Deterministic Kleene Coalgebras

In this paper, we present a systematic way of deriving (1) languages of (generalised) regular expressions, and (2) sound and complete axiomatizations thereof, for a wide variety of systems. This generalizes both the results of Kleene (on regular languages and deterministic finite automata) and Milner (on regular behaviours and finite labelled transition systems), and includes many other systems such as Mealy and Moore machines.

Finite-State Controllers Based on Mealy Machines for Centralized and Decentralized POMDPs

Existing controller-based approaches for centralized and decentralized POMDPs are based on automata with output known as Moore machines. In this paper, we show that several advantages can be gained by utilizing another type of automata, the Mealy machine. Mealy machines are more powerful than Moore machines, provide a richer structure that can be exploited by solution methods, and can be easily incorporated into current controller-based approaches. To demonstrate this, we adapted some existing controller-based algorithms to use Mealy machines and obtained results on a set of benchmark domains. The Mealy-based approach always outperformed the Moore-based approach and often outperformed the state-of-the-art algorithms for both centralized and decentralized POMDPs. These findings provide fresh and general insights for the improvement of existing algorithms and the development of new ones.

Intuitionistic Linear-Time μ-Calculus

线性mu-演算(μTL)是线性时序逻辑(LTL)的不动点扩展.LTL是一个便于规范和论证反应式系统的方法.μTL作为比LTL表达能力更强的逻辑,用LTL表示的性质度可由μTL表示.类似于LTL的直觉线性时序逻辑(LTL),提出一种基于直觉解释的μTL,称为直觉μTL(IμTL).确立了IμTL和ILTL的关系,比较了它们之间的表达能力.讨论了使用IμTL与安全性质和活性描述的关系以及描述“假设-保证”规范的问题.

FlexRFID: A design, development and deployment framework for RFID-based business applications

The surge of RFID technology and ensuing competition in the RFID vendor market has increased the complexity of integration of RFID into current business processes. To address this problem, we present FlexRFID, a modeling template composed of state indicators, conditions, a simulation engine, and a device-independent deployment architecture for rapid prototyping of control applications using RFID and sensor hardware. The modeling technique is based on Moore Machines, a variant of finite state automata that allow states to be associated with outputs. With FlexRFID, users design applications by modeling business logic via transition of states based on sensor events. Outputs associated with individual states can handle operational characteristics of the application. In this article, we present the modeling methodology and demonstrate how organizations can develop complex applications easily using FlexRFID. We believe that the simplicity and flexibility of FlexRFID will lead to the development of RFID applications quickly even with limited resources. In addition, the parking entry application presented in our paper demonstrates FlexRFID's capability of being used in business application context, as well as in research, training, and teaching.