9

Finite State Automata

In this chapter, we study abstract models of machines that can accept input, produce output and have primitive internal memory to keep information about previous inputs. In these machines, the output depends not only on the input but also on the state of the system at the time the input is introduced.

9.1 FINITE STATE MACHINES

Definition 9.1

A finite state machine (complete sequential machine) is an abstract model of a machine with a primitive internal memory. A finite state machine M consists of

  1. A finite set of I input symbols
  2. A finite set S of “internal” states
  3. A finite set O of output symbols
  4. An initial state s0 in S
  5. A next-state function f : S × IS
  6. An output function g: S × I0

A finite state machine M is ...

Get Discrete Mathematics, 1st Edition by Pearson now with the O’Reilly learning platform.

O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.