Sequential program, state machine, Concurrent process models

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1 INSIGHT Sequential program, state machine, Concurrent process models Finite State Machines, or automata, originated in computational theory and mathematical models in support of various fields of bioscience. However, their popularity today in the computer science and engineering fields can be attributed to the pioneering efforts of George H. Mealy and Edward F. Moore performed at Bell Labs and IBM (circa 1960s). Mealy and Moore's Finite State Machine concepts proved valuable in two important engineering disciplines: language parsing (compilers) and sequential circuit design. Gradually, the software engineering community partially adopted FSM concepts as more structured analysis and design methods were needed to validate this originally arcane endeavor.the word automaton itself, closely related to the word "automation", denotes automatic processes carrying out the production of specific processes. Simply stated, automata theory deals with the logic of computation with respect to simple machines, referred to as automata. Through automata, computer scientists are able to understand how machines compute functions and solve problems and more importantly, what it means for a function to be defined as computable or for a question to be described as decidable. Automatons are abstract models of machines that perform computations on an input by moving through a series of states or configurations. At each state of the computation, a transition function determines the next configuration on the basis of a finite portion of the present configuration. As a result, once the computation reaches an accepting configuration, it accepts that input. The most general and powerful automata is the Turing machine. The major objective of automata theory is to develop methods by which computer scientists can describe and analyze the dynamic behavior of discrete systems, in which signals are sampled periodically. The behavior of these discrete systems is determined by the way that the system is constructed from storage and combinational elements. Characteristics of such machines include: Inputs: assumed to be sequences of symbols selected from a finite set I of input signals. Namely, set I is the set {x1, x,2, x3... xk} where k is the number of inputs.

2 Outputs: sequences of symbols selected from a finite set Z. Namely, set Z is the set {y1, y2, y3... ym} where m is the number of outputs. States: finite set Q, whose definition depends on the type of automaton. There are four major families of automaton : Finite-state machine Pushdown automata Linear-bounded automata Turing machine The families of automata above can be interpreted in a hierarchal form, where the finite-state machine is the simplest automata and the Turing machine is the most complex. The focus of this project is on the finite-state machine and the Turing machine. A Turing machine is a finite-state machine yet the inverse is not true. The exciting history of how finite automata became a branch of computer science illustrates its wide range of applications. The first people to consider the concept of a finite-state machine included a team of biologists, psychologists, mathematicians, engineers and some of the first computer scientists. They all shared a common interest: to model the human thought process, whether in the brain or in a computer. Warren McCulloch and Walter Pitts, two neurophysiologists, were the first to present a description of finite automata in Their paper, entitled, "A Logical Calculus Immanent in Nervous Activity", made significant contributions to the study of neural network theory, theory of automata, the theory of computation and cybernetics. Later, two computer scientists, G.H. Mealy and E.F. Moore, generalized the theory to much more powerful machines in separate papers, published in The finite-state machines, the Mealy machine and the Moore machine, are named in recognition of their work. While the Mealy machine determines its outputs through the current state and the input, the Moore machine's output is based upon the current state alone.

3 An automaton in which the state set Q contains only a finite number of elements is called a finite-state machine (FSM). FSMs are abstract machines, consisting of a set of states (set Q), set of input events (set I), a set of output events (set Z) and a state transition function. The state transition function takes the current state and an input event and returns the new set of output events and the next state. Therefore, it can be seen as a function which maps an ordered sequence of input events into a corresponding sequence, or set, of output events. State transition function: I Z ANALYSIS Read about the basics of turing machine in the link given below to understand the analysis subsection Conceptually a Turing machine, like finite automata, consists of a finite control and a tape. At any time it is in one of the finite number of states. The tape has the left end but it extends infinitely to the right. It is also divided into squares and a symbol can be written in each square. However, unlike finite automata, its head is a read-write head and it can move left, right or stay at the same square after a read or write.

4 Given a string of symbols on the tape, a Turing machine starts at the initial state. At any state it reads the symbol under the head, either erases it or replaces it with a symbol (possibly the same symbol). It then moves the head to left or right or does not move it and goes to the next state which may be the same as the current state. One of its states is the halt state and when the Turing machine goes into the halt state, it stops its operation. Hence a turing machine is : Simple machine with N states. Start in state 0. Input on an arbitrarily large TAPE that can be read from *and* written to. Read a bit from tape.

5 Depending on current state and input bit write a bit to tape move tape right or left move to new state Stop if enter Yes or No state. Accept if yes, reject if no or does not terminate Therefore, the major difference between a Turing machine and two-way finite automata (FSM) lies in the fact that the Turing machine is capable of changing symbols on its tape and simulating computer execution and storage. For this reason, it can be said that the Turing Machine has the power to model all computations that can be calculated today through modern computers. IMAGINATION Imagine that the elevator is for a preschool and kids tend to press a lot of these buttons.you should consider only the button pressed by the security or caretaker.how would a power efficient design for the above variant be like? You could also come up with other alternatives like elevator door will open only if a person is waiting outside (hence put a human sensor ) or it will remain open dependant on the number of people who wish to exit at that floor. Also, design a real time system for it. (Hint : statecharts are real time implementations of FSM ) The following information may come useful: Petri nets

6 A powerful technique for specifying systems that have potential problems with interrelations A Petri net consists of four parts: A set of places P A set of transitions T An input function I An output function O Try to come up with a petri net implementation of your elevator design. (Hint : refer Sixth Edition, WCB/McGraw-Hill, 2005 )