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Understanding Finite Automata with Output in Automata Theory: Moore and Mealy Machines

Dive into the world of finite automata with output through Moore and Mealy machines, two distinct types of machines created by G.H. Mealy in 1955 and E.F. Moore in 1956. Explore the components of Moore machines, their transition and output tables, and the unique characteristics of Mealy machines. Discover how these machines are utilized as mathematical models for sequential circuits in computer architecture. Practice your knowledge with exercise questions from Chapter 8.

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Understanding Finite Automata with Output in Automata Theory: Moore and Mealy Machines

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  1. CSC312 Automata Theory Lecture # 17-18 Chapter # 8 by Cohen Finite Automata with Output

  2. The are two types of machine (FAs) with output capabilities. These are create by G.H Mealy (1955) and, independently by E.F Moore (1956). The original purpose of the inventors was to design a mathematical model for sequential circuits, which are only one component of the architecture of a whole computer. • Moore Machine: • A Moore machine is a collection of five things • An alphabet of letters ={a, b, c,… } from which the input strings are formed. • An alphabet  = {x, y, z,…} of possible output characters.

  3. Moore Machine (Cont…) • 3) A finite set of states q0, q1, q2,... Where q0 is the initial state. • 4) A transition table that shows for each state and each input letter what state is reached next. • 5) An output table that shows what character from  is printed by each state as it is entered. • Note: • The Moore machine prints the output character of start state even before looking at the input letter.

  4. Moore Machine (Cont…) • 2) Since there is no state designated to be a final state, so there is no question of accepting any language by Moore Machine. • 3) The state to be initial is not important as if the machine is used several times and is restarted after some time, the machine will be restarted from the state where it was left off. • Ex:

  5. Mealy Machine • A Mealy machine is a collection of four things • An alphabet of letters ={a, b, c,… } from which the input strings are formed. • An alphabet  = {x, y, z,…} of possible output characters. • A finite set of states q0, q1, q2,... where q0 is the initial state. • A pictorial representation with states represented by small circles and directed edges indicating transitions between states. Edges are labeled by an input letter along with an output character in the form i/o. Every state must have exactly one outgoing edge for each possible input letter.

  6. Mealy Machine (Cont…) • Note: • The Mealy machine no state is designated to be a final state, so there is no quesiton of accepting any language. • The state of the initial is not important as if the machine is used several times and is restarted after some time, the machine restarted after some time, the machine will be restarted from the state where it was left off. • Ch # 8: Exercise Questions 1, 3, 4, 6, 7, 8, 9

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