Finite state automata

Many individual finite state automata are joined together to form a regular array in one, two, or more dimensions this entire array is the cellular automaton. The CA evolve, as all cells in this array update their state synchronously. Into each cell is fed a small amount of input provided by its neighbors. Taking account of this input, the cell then generates some output, which determines the next state of the cell in deciding what its output should be, each cell consults its state, which consists of one piece, or a few pieces, of information stored within it. In the most elementary of automata, the state of the cell that comprises this finite state automaton is very simple, perhaps just... 

Timed Automata (TA) are finite state automata extended by the notion of clocks to model discrete event systems with timed behaviour. A timed automata is defined by a tuple, TA = ( i, C, 0, inv, Iq, F) in which, L represents the finite set of discrete locations, lo, F G L, where Iq represents the initial location and F represents the set of final locations. The set of clocks assigned to the TA are represented by C. The relation 0 C iX XActXU(C)XL represents the set of transitions between the locations where, is a set of guards specified as conjunctions of constraints of the... 

Behavior generation. RCS way of generating behavior seems best for discrete or semi-continuous systems (usually implements finite state automata). There is no documented application of RCS for large continuous processes. Some adaptation on how to exploit the knowledge should be done (for process systems, knowledge is strongly based in laws and equations so numerical techniques to deal with them should be available). 

The most currently used state space models in the context dependability studies are (Cassandras Lafortune 2008) Finite State Automata and Language theory, Petri Nets and Markov chains. Other models can also be mentioned in the context of... 

Kondacs, A., Watrous, J. On the power of quantum finite state automata. In 38th IEEE Conference on Foundations of Computer Science, pp. 66-75. IEEE Computer Society Press, Los Alamitos (1997)... 

Based on the prineiples defined indiftereutly in the form of diode diagrams, relay diagrams, or eqirations, GRAFCET, Block Diagram, a transcript as finite state automata (AEFD model) is performed. The initialization phase and degraded modes are taken into account by successive refinement. We thus have an unambiguous description of processes to be done under the control of the host stmeture, a library of standard actions and a principle of unique resolution the runtime of finite state automata. 

Although there is the possibility of confusion in terminology when dealing with the applications of CA, since they are often applied to the simulation of processes that involve biological cells, we shall follow standard practice and refer to both the finite state automaton and the place in which it is located as a "cell."... 

A finite state automaton is also known as a finite state machine. 

Fig. 2.11 Hybrid bond graph of the bouncing ball problem and a finite state automaton associated...

A technological system, a machine, can be formally described as a finite state automaton or a state machine in terms of a set of inputs, outputs, internal states, and state transitions. But such a description also forces designers (and managers) to think of humans in the same way. In order for the machine to work and produce a pre-defined output, it must get a correct input. This means that the user must respond in a way that corresponds to the pre-defined categories of input. It is also necessary that the output is correctly interpreted by the user, i.e., that it can be correctly mapped onto one of the pre-defined response possibilities. If the user fails to accomplish that, i.e., if the user s response is not included in the expected set of responses, the system will in effect malfunction. 

ABSTRACT In dependability studies of dynamic systems it is important to assess the probability of occurrence for the events sequences which describe the system evolution or which are critical for the mission of the system or for the humans and environment safety. In this paper we use the probabilistic languages framework in order to realize the quantitative assessment and we start by modeling the system as a finite state automaton. This is ulterior transformed in a probabilistic automaton using the embedded discrete Time Markov Chain. The determination of the languages afferents at each state of the automaton enable to calculate the probabihty of occurrence for every events sequence that can be subtract from these languages. 

In this paper, we presented the use of the theory of probabilistic language for the assessment of the occurrence probability of events sequences that describe the system evolutions. In order to be able to apply this theory, for a system modelled by a finite state automaton, we proposed a 3 steps approach. 

In order to extract these MCS, we use the algorithms defined in Chaux et al. (2011) and Chaux et al. (2012). The first one transforms a BDMP model into a finite state automaton and the second one extract the MCS of a finite state automaton. Several MCS limited to the length 5 (selected arbitrary among the 84 existing) extracted... 

The SYMEL or PIPC computerized interlocking module has been developed to control the level of safety and reduce the costs of maintenance in operational condition. To do this, we defined a specification interpretation language, the deterministic finite state automaton (AEFD Automate a Etats Finis Deterministe) language. 

The model of specifications used (finite state automaton) requires the definition of a graphical representation of automata and operation for the rantime system (algorithm for resolution and stabilization). For this, we use a drawing tool coupled with a database. 

Although CA are most often assumed to live 011 infinitely large lattices, we can equally well consider lattices that are finite in extent (which is done in practice regardless, since all CA simulations are ultimately restricted by a finite computer memory). If a lattice has N sites, there are clearly a finite number,, of possible global configurations. The global dynamical evolution can then be represented by a finite state transition graph Gc, much like the one considered in the description of an abstract automaton in section 2.1.4. 

DEFINITION A finite automaton M. is specified by three sets A, E and E and a state-transition function 0 E x A E, where... 

Given an automaton M that starts in state CTi, and any finite string s A, a, s) will represent the final output state that J<4 will enter after having processed s, one symbol at a time, from left to right. J<4 is said to accept the word s if ai,s) E the word s is rejected if and only if it is not accepted. Finally, we may define the language C JA) accepted by M as the set of all words s A that are accepted by Ad. A language C is called regular if there is a finite automaton Ad that accepts it. 

Abstract automata are machines with internal states, an input tape, and sometimes an auxiliary information storage stack. Automata read symbols from the tape, making transitions from one state to another, while performing other operations on the tape and stack. The simplest example of such an idealized machine is the finite automaton ... 

DEFINITION A push -down automaton A4 is specified by four sets A, E, A and E and a finite set of state-transition functions 3 cp T, x A T, where... 

Fig. 12.18. Schematic of the coupling between a finite element treatment of heat transfer and the cellular automaton treatment of the grain structure (adapted from Gandin and Rappaz (1994)). The top frame shows the finite element mesh and the lower frame shows the lattice of points used to do bookkeeping concerning the state (liquid or solid) and orientations of the associated points.

General class of algorithmic methods that involve a stochastic element, i.e., that let the computer make random decisions (Binder Landau, 2000). An important subclass, the so-called Markov Chain Monte Carlo (MCMC) methods can be understood as acting on Markov chains. A Markov chain is a stochastic finite automaton that consists of states and transitions between states (Feller, 1968). At each time we consider ourselves as resident in a certain state of the Markov chain. At discrete time steps we leave this state and move to another state of the chain. This transition is taken with a certain probability characteristic for the given Markov chain. The probability depends only on the two states involved in the transition. Often one can only move to a state in a small set of states from a given state. This set of states is called the neighborhood of the state from which the move originates. 

The main objective of the study is the abUily to analyze an identified model in identifying automaton models from observations. We want to take an established method to learn a DFA and apply it to our timed sequences. Our problem could be modelled as a timed-state transition graph, a probabilistic deterministic finite automaton (PDFA) taking into account timed-event. We also have a set of positive timed-strings (or time-stamped event sequences). 

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