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.

**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

- A finite set of
*I***input symbols** - A finite set
*S*of “**internal**” states - A finite set
*O*of**output**symbols - An initial state
*s*_{0}in*S* - A next-state function
*f*:*S*×*I*→*S* - An output function
*g*: S ×*I*→*0*

A finite state machine *M* is ...

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