Moore machine

A Moore machine (named after the mathematician Edward F. Moore ( 1925-2003 ) ) is a finite state machine, which can be deterministic or non-deterministic. In contrast to the Mealy automaton its output only depends on its condition. When you reach a state of an output is generated, which is independent of the transition to this state.

Formal definition

The Moore machine can be defined as a 7- tuple:

• Is a finite set of states.
• Is the input alphabet. ,
• Is the output alphabet.
• Is the transfer function
• Defines the output function:
• Is the start state.
• Is a (finite ) set of possible accepting states ( = final amount ). When the machine stops in a state of after reading the input word, as part of the language.

If the regular language of the machine is of no interest, can also be omitted. Then, the machine is defined as a 6- tuple.

The number of states of a Moore machine is not less than the number of states of the corresponding Mealy machines.

Digital technology

A realization of the Moore machine is possible using digital technology. For this purpose, two switching networks and a clocked memory block are required. In addition to the wired on a PCB logic blocks, the implementation is often performed by means of programmable logic and application of a hardware description language.

The processing of logic circuits requires the conversion of the input and output alphabet in a binary code similar to the following table.

Description of an automaton

Given a region defined by a 6- tuple of deterministic finite automaton with

,

,

And.

The transition function and the output function can be represented by a graph or an automatic machine table.

Both the graph and the table can now see information such as the following:

When the machine is in the state, and from there the character " x " or the "Z" character is reading, the machine goes into the state. Upon reaching the state of the output "c" occurs.

Transfer to a Mealy automaton

Each Moore machine can very easily be converted into an equivalent Mealy automaton. For this purpose, only the output symbol of the target state with the transition ( state transition ) must be written. Let us consider the above example, then the transfer is as follows: