A finite state transducer is is a finite state automaton in which
the members of 
are pairs, triples, etc., rather than simple symbols.
Traditionally the members of are just pairs, of which the left-hand
member is the `input symbol' and the right-hand member is the `output symbol'.
A deterministic finite state transducer (DFST) is defined as a septuple
, where:
  Q | [ initial state] |
| Q | [ finite set of states ] |
F  Q | [ subset of Q of final states ] |
|
| [ finite set of input symbols ] |
 | [ finite set of output symbols ] |
 | [ finite set of transitions between states ] |
 | [ finite set of transductions to symbols ] |
Sometimes 
and 
are combined: 
.
A nondeterministic finite state transducer (NFST) is defined as a sextuple
, where:
|
Q | [ initial state] |
| Q | [ finite set of states ] |
|
F Q | [ subset of Q of final states ] |
|
| [ finite set of input symbols ] |
|
| [ finite set of output symbols ] |
|
| [ finite set of transition-transductions to sets of state-symbol pairs ] |