Place automata

Following the above observations, the process model can be formulated by TA. For formal definitions of the syntax and semantics of TA, see [15]. TA are used to model the individual resources by resource automata and to describe timing constraints by place automata. The former are used to start and to finish tasks which are uniquely assigned to resources, the latter establish timing constraints of places. 

Special clock variables called docks a, i = 1,..., NC are used to measure the time between events. The values of the clocks increase permanently with the rate t = 1. Clocks are used to measure the durations of tasks for the resource automata, and to measure the waiting between two tasks for place automata. 

Fig. 10.4 The timed automata models of the resources Ri, R2, R3 and the place automaton Pi.

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."... 

An even more drastic simplification of the dynamics is made in lattice-gas automaton models for fluid flow [127,128]. Here particles are placed on a suitable regular lattice so that particle positions are discrete variables. Particle velocities are also made discrete. Simple rules move particles from site to site and change discrete velocities in a manner that satisfies the basic conservation laws. Because the lattice geometry destroys isotropy, artifacts appear in the hydrodynamics equations that have limited the utility of this method. Lattice-gas automaton models have been extended to treat reaction-diffusion systems [129]. 

Fig. 7.16. Operation of a cellular automaton-a model of gas. The particles occupy the lattice nodes (cellsl. Their displacement from the node symbolizes which direction they are heading on with the velocity equal to 1 length unit per 1 time step. In the left scheme (a), the initial situation is shown. In the right scheme the result of the one step propagation and one step collision is shown. Collision only took place in one case (at 03 2). collision rule has been applied (of the lateral outgoing). The game would...

Before showing how this can be done, we must first define more precisely what a cellular automaton (CA) is. A CA model for a system is constructed as follows The dynamical evolution is imagined to take place on a set of cells. Each cell is defined by a finite set of values of a dynamical variable = sk-k = l,...,n. The values of the s in a cell change at discrete time instants according to a rule that depends on the value of s in the cell as well as that of its neighbors. Even very simple rules, 3i, can produce complicated dynamics. In fact, CA rules that are Turing machines, that is, are capable of universal computation, can be devised. 

Chemically reacting systems typically involve reactions among many chemical species and there is a number of ways to construct mult-component lattice-gas automaton models for example, one may place all species on a single lattice or one may consider a collection of lattices, one for each chemical species. There is a number of technical reasons why it is convenient to... 

The I/O software unit (LUES Logiciel Unite Entrees/Sorties), running on the UES card that manages the 1553 transfer of the frame and aperiodic transfers (immediate or dated), is an automaton based on the Aonix SMART executive. It manages the frame distributed on the two 1553 buses from information provided in the tables programmed in advance and placed in the exchange memory UT/UES. 

The tape unit consists of a tape control and a tape. The tape is a linear array of cells that contains the information about M, the automaton to be constructed. In particular, it contains (in left-to-right order) (1) the x and y coordinates xo,yo) of the lower left-hand corner of the rectangle in which the new automata is to be constructed (the construction area ) (2) the width a and height /3 of that rectangle and (3) the cell states making up the automaton (listed in reverse order of where they are to be placed in the rectangle) and a asterisk indicating the end of the tape. 

The original automaton Me is turned on by an external signal sent to the construction control. The construction control then sends a signal to the tape unit, which reads from the tape and sends (via signals) the values of xq, yo, oc, and p to the construction control. The construction control then causes the construction arm —an expanding and contracting array of cell states—to move (by changing the states of intermediate cells) from its initial position to the upper left-hand corner of the construction area. Then the construction control asks for and receives the value of successive states on the tape, and moves the construction arm to place them in their proper positions in the construction area. 

---