Finite State Automaton Model Research Articles

Techniques for the Parametrization of Discrete-Event System Templates

Two techniques for the parametrization of templates in the template design methodology are introduced. First, the use of finite-state automata extended with variables is demonstrated. This kind of parametrization allows one to vary the occurrences of events by varying a parameter. Second, a new way of parametrizing templates is proposed, named compositional parametrization. With this technique, a template consists of the composition of a number of structurally identical components whose events are indexed differently, depending on a parameter. This kind of parametrization allows one to vary the structure and event set of the template by varying a parameter. An enhancement of compositional parametrization with the use of special selector transitions is also discussed. This extension allows one to model interactions between components which depend on the total number of components in a composition and thus cannot be modelled by simple parametrization of event indices. With the choice of a specific parameter, regular finite-state automaton models are obtainable from the templates parametrized with any of the aforementioned techniques. Thus, such parametrized templates can be easily introduced in the template design modelling environment and they integrate seamlessly with the supervisory control framework. Motivating examples to illustrate the application of template parametrization are provided.

Using finite state automata (FSA) for formal modelling of affordances in human-machine cooperative manufacturing systems

Modelling complex systems poses significant challenges on how one represents the system components and interactions among them. In order to provide a systematic approach to represent human participation as a part of a dynamic system, this paper presents a formal automata model of human-machine cooperative systems that incorporates human capabilities with respect to system conditions. Specifically, we propose a control model for human-involved shop floor systems based on discrete event-based systems (DES) and an environmental concept known as an affordance. When modelling human-involved systems where a human operator is considered a crucial system component, it is necessary to analyse the model complexity that increases significantly due to a human's behavioural patterns. From the perspective of the temporal and physical state domains a human operator's behaviour is usually limited by attention and resource constraints. We investigate these limitations and map them into constrained system affordances, and then construct a formal human-machine cooperative model based on the finite state automaton (FSA) model. The proposed model can provide a framework to combine human activities into systems operations in consideration of human's effectivities and system affordances. A detailed application example is provided to illustrate that the proposed model can effectively be applied to manufacturing control systems.

Autonomous robot navigation using optimal control of probabilistic regular languages

This paper addresses autonomous intelligent navigation of mobile robotic platforms based on the recently reported algorithms of language-measure-theoretic optimal control. Real-time sensor data and model-based information on the robot's motion dynamics are fused to construct a probabilistic finite state automaton model that dynamically computes a time-dependent discrete-event supervisory control policy. The paper also addresses detection and avoidance of livelocks that might occur during execution of the robot navigation algorithm. Performance and robustness of autonomous intelligent navigation under the proposed algorithm have been experimentally validated on Segway RMP robotic platforms in a laboratory environment.

LABELLING MULTI-TAPE AUTOMATA WITH CONSTRAINED SYMBOL CLASSES

Rational relations are a powerful model used in many domains such as natural language processing. In this article, we propose a new model of finite state automata: multi-tape automata with symbol classes and identity or non-identity constraints. This model generalizes classical multi-tape automata, as well as automata and transducers with extended alphabet. We define this model in terms of a constraint satisfaction problem and discuss a problem occurring when handling the projection operation. Finally, we describe its implementation and results of a performance test.

Diagnosing PN-based models with partial observable transitions

Failure diagnosis back-traces failures based on an observed system behaviour when a failure occurs. Ushio et al. (1998) first studied the diagnosability of Petri net (PN) models, a common mathematical modelling structure for CIM systems. With transitions all assumed to be unobservable, the diagnosis process of Ushio et al. relies solely on marking changes at observable places, making diagnosability analysis of most non-trivial PN non-diagnosable. However, in the context of manufacturing process, the initiation of a command and the response of a process are readily available to supervisory controller. This paper, in contrast, assumes that part of the transitions of the PN modelling is observable. Under this assumption, the first contribution of this paper is to investigate how both the label propagation function and the range function, used to construct a diagnoser, are to be revised in order to take advantage of the newly available information provided by observable transitions. The second contribution is to present a procedure to construct, for PN modelling, the associated verifier, first proposed by Yoo and Lafortune (2001) as a polynomial check mechanism on diagnosability but for finite state automata models. As shown by examples, the additional information from observed transitions in general adds diagnosability to the analysed system.

Optimal supervisory control of finite state automata

This paper presents optimal supervisory control of dynamical systems that can be represented by deterministic finite state automaton (DFSA) models. The performance index for the optimal policy is obtained by combining a measure of the supervised plant language with (possible) penalty on disabling of controllable events. The signed real measure quantifies the behaviour of controlled sublanguages based on a state transition cost matrix and a characteristic vector as reported in earlier publications. Synthesis of the optimal control policy requires at most n iterations, where n is the number of states of the DFSA model generated from the unsupervised plant language. The computational complexity of the optimal control synthesis is polynomial in n. Syntheses of the control algorithms are illustrated with two application examples.

Automatic Implementation and Verification of Coordinating PLC-Code for Robot Cells

A method for automatically generating the coordinating PLC-code for a multi-robot cell is presented. Finite state automaton models of the allocation and release of the spatial volumes that the robots share, as well as the sequences of each robot's allocations, are automatically extracted from a 3D simulation environment. This includes explicitly calculating the intersection between the robots' work envelopes, the spatial volumes where collisions may occur. The system model is then analyzed using the Ramadge-Wonham supervisory control theory to verify collision freeness and nonblocking. If necessary, a maximally permissive supervisor that guarantees these properties can be synthesized. The supervisor will include the necessary interlocks but in doing so still permits the robots as much freedom as possible. Thus, if one robot is delayed, the other robots may be free to book and enter a spatial volume that they normally would have to wait for. Finally, from the synthesized supervisor, PLC-code to be run in a controller for coordination of the robots is generated.

A finite state automaton model for multi-neuron simulations

‘Classical’ compartmental modelling techniques involve numerical solution of large sets of ordinary differential equations (ODEs). The computational cost of neuronal network evaluation using these techniques forms a major bottleneck in the exploration of the effects of dendrite morphology on network functionality. To reduce computational load, we have developed a finite-state automaton model of membrane activity, which will potentially permit the evaluation and comparison of large numbers of simulated 3-dimensional networks. The automaton mimics the behaviour of 2-equation ODE models for wave propagation in excitable media, and was found to be capable of modelling the most important characteristics of neural membranes.

Computing Approximating Automata for a Class of Hybrid Systems

This paper presents a new algorithm for generating finite-state automata models of hybrid systems in which the continuous-state dynamics can be switched when the continuous-state trajectory generates threshold events. The automata state transitions correspond to threshold events and the automata states correspond to portions of the threshold surfaces in the continuous state space. The hybrid system dynamics are approximated by the automata models in the sense that the languages of threshold event sequences generated by the automata contain the threshold event language for the hybrid system. Properties of the algorithm for constructing and refining the approximating automata are demonstrated and the application of approximating automata for system verification is illustrated for a switching controller for an inverted pendulum. Relationships to other approaches to hybrid system synthesis and verification are also discussed.

A finite automata approach to modeling the cross product of interconnection networks

This paper describes a modeling technique, finite state automata (FA) model, for the cross product of interconnection networks. The primary purpose of the proposed modeling technique is to provide a mechanism for developing efficient routing and novel embedding algorithms, which we refer to as node-independent algorithms, for product networks. In contrast to the current embedding algorithms which are node dependent (their output is a set of adjacent node labels which forms the desired topology), the embedding algorithms developed in this paper are rule-based. That is, they generate a set of rules (input sequences to the FA model of the network) which can be used by any node for mapping a desired topology into the network. Furthermore, a new interconnection topology, called Ring Connected Cycles (RCC), is introduced. The main objective of introducing RCC networks is to illustrate the use of the FA model to develop node-independent embedding as well as routing algorithms. In addition, to demonstrate the generality of the proposed technique, FA models of several popular interconnection networks (such as n-cubes and n-star graphs) are presented. The RCC networks are proposed in this paper as a possible communication network for parallel multicomputers or as an alternative to the ring topology for local area networks. An RCC network can execute grid, mesh and ring algorithms as efficiently as the grid, mesh, and ring networks. It is shown in Section 6 that this significant amount of computational versatility offered by RCC networks comes at no additional VLSI area cost over the same size ring, grid, or mesh networks.

A Real-Time Realization Of Fault-Detection And Diagnosis Using Finite-State Automaton

This paper addresses the problem of Fault-detection and Diagnosis using Finite-state Automaton Models (FAM). These models partition the state-space into finite regions and contain information on system trajectory within these regions. A framework for modeling faults using FAM is discussed. A Fault-detection engine is then developed to detect and isolate faults. The algorithm is illustrated with a case study.

Evolution of Strategies in the three-person Iterated Prisoner's Dilemma Game

A three-person iterated prisoner's dilemma (3p-IPD) game is studied. The present simulation uses a lattice model of finite state automata. In particular, the similarity between a noisy 2p- and a noiseless 3p-IPD game is discussed. It is known that, due to the noise, Tit for Tat loses its robustness and is taken over by more complex strategies in a noiseless IPD game. But in the 3p-IPD game, even without noise, Tit for Tat loses its robustness and is also taken over by more complex strategies. It is found that similar strategies take over Tit for Tat in both situations. We thus remark that the role of noise in the two person game is replaced by the third player in the three-person game. As a result, the strategies diversify in both the noisy 2p- and the quiet 3p- IPD game. It is also found that game strategies in an automaton form can be understood as a combination of defensive and offensive substructures. A recognition of these substructures enables us to study the mechanism of robustness in the strategies of the 3p-IPD game.

Simulation of Diffusion Phenomena by Cellular Automata

This paper describes a new simulation technique for diffusion phenomena over the sea surface using Cellular Automata (CA), which is capable of making prediction of oil dispersion from tankers come into collision or stranded on rocks. Automaton is known as an abstract expression of sequencial machine in the field of information science, and CA is recognized as one of the model of finite state automata with sectional analysis domain called “cell”. CA has also been applied to demonstrate various engineering phenomena, and one of the most promising application field is flow simulation of viscous fluid, percoration, multi-phase fluid, reaction diffusion problems and so on. In this field, CA is called Lattice Gas Automata (LGA) and the solutions by LGA has been proved to coinside those by Navier-Stokes equation. In the procedure of CA, the analytical area is devided into cells and all the state variables defined on each cell are made transition by local neighbor rule and transition rule along the discrete time steps without solving the governing equation.In the present paper, CA is applied to solve a diffusion problem in which the simulation results are compared to the analytical solution of diffusion equation, and possibility is shown in predicting the oil dispersion in the accident of tanker occured in Japan Sea in January, 1997, as an example. It is shown that the simulation by CA shows good agreement with the analytical solution of diffusion equation, and that the prediction of oil dispersion in Japan Sea can be made in a short time by a personal computer.

A COLOSSAL FISH

A finite state automaton model for the operational principles of the German WWII SZ40/42 encryption machine and the mathematical principles lying behind the key generation of the SZ40/42 are tentatively reconstructed from secondary historical sources. Special statistical properties of BAUDOT-coded German language are exploited in a cryptanalytical attack which can in turn explain the principal operations performed with the British COLOSSUS machines.

Testing from a Z Specification

This paper looks at the formal analysis of Z specifications in order to enhance the testing process. An algorithm is given that rewrites the specification to a form from which both a partition of the input domain and the states of a finite state automaton model can be derived. Test cases can be derived from the former and an automated system to control the testing process can be based upon the latter. © 1997 by John Wiley & Sons, Ltd.

Extending Test Sequence Overlap by Invertibility

Finite state automata can be used to model a system; in particular they can be used to model the control section of a communications protocol. A number of authors have produced algorithms that represent the problem of minimizing the testing against a finite state automaton model as a max flow/min cost problem for an associated network. We extend this work by introducing the use of invertibility to utilize test sequence overlap.

Machine Models for Cognitive Science

Introduction. During the past two decades philosophers of psychology have considered a large variety of computational models for philosophy of mind and more recently for cognitive science. Among the suggested models are computer programs, Turing machines, pushdown automata, linear bounded automata, finite state automata and sequential machines. Many philosophers have found finite state automata models to be the most appealing, for various reasons, although there has been no shortage of defenders of programs and Turing machines. A paper by Arthur Burks (1973) convinced me long ago that “all natural human functions” are, or can be fruitfully modeled to be, finite state automata with output. Further work in the field has reinforced this conviction. There is room, however, for the use of any of the above models in philosophy of mind and in the ongoing development of cognitive science.