12/31/2023 0 Comments Finite automatonIts main application is in mathematical problem analysis. This mathematical model of a machine can only reach a finite number of states and transitions between these states. 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.įinite-state machines are ideal computation models for a small amount of memory, and do not maintain memory. The state transition function takes the current state and an input event and returns the new set of output events and the next state. 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. 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.Īn automaton in which the state set Q contains only a finite number of elements is called a finite-state machine (FSM). The finite-state machines, the Mealy machine and the Moore machine, are named in recognition of their work. Moore, generalized the theory to much more powerful machines in separate papers, published in 1955-56. 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. Warren McCulloch and Walter Pitts, two neurophysiologists, were the first to present a description of finite automata in 1943. They all shared a common interest: to model the human thought process, whether in the brain or in a computer. 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. The exciting history of how finite automata became a branch of computer science illustrates its wide range of applications. A Turing machine is a finite-state machine yet the inverse is not true. The focus of this project is on the finite-state machine and the 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. There are four major families of automaton : States: finite set Q, whose definition depends on the type of automaton.Namely, set I is the set where m is the number of outputs. Inputs: assumed to be sequences of symbols selected from a finite set I of input signals.Characteristics of such machines include: The behavior of these discrete systems is determined by the way that the system is constructed from storage and combinational elements. 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 most general and powerful automata is the Turing machine. As a result, once the computation reaches an accepting configuration, it accepts that input. At each state of the computation, a transition function determines the next configuration on the basis of a finite portion of the present configuration. Īutomatons are abstract models of machines that perform computations on an input by moving through a series of states or configurations. 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. Simply stated, automata theory deals with the logic of computation with respect to simple machines, referred to as automata. The word automaton itself, closely related to the word "automation", denotes automatic processes carrying out the production of specific processes. It established its roots during the 20th Century, as mathematicians began developing - both theoretically and literally - machines which imitated certain features of man, completing calculations more quickly and reliably. Automata Theory is an exciting, theoretical branch of computer science.
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