Lossless machine learning: constructing a single symbol output transducer  from input word,
output symbol pairs by logic programming.
In other words, constructing a Moore-machine. https://en.wikipedia.org/wiki/Moore_machine
There are several implementations for representing the transducer. These are the common functions.
delta - the state transition table is a nested associative data structure (map or vector)
(delta input) gives a transformation of the state set

FIXED OUTPUT TRANSDUCER CONSTRUCTION
This is the first working version of transducer synthesis so it is somewhat of
a legacy code. The input-output pairs need to be given in the internal representation
(nonnegative integers) thus the output of the Moore automaton is hardcoded.
Consequently, there is the issue of using the initial state 0 as an output which may be a too
rigid constraint.

FLEXIBLE INPUT OUTPUT TRANSDUCER CONSTRUCTION
input words can be sequences of any type of distinct entities
similarly outputs can be of any types
internal states are nonnegtaive integers

To find partially defined transducers, this method has the states in all
trajectories as the logic variables. Then the individual maps are extracted
and used to define the partial transformations.
This method is inefficient as complexity of the search grows with the number 
and the length of the input words.

Algorithm for minimizing a transducer.

A custom implementation of a search trie with the added feature that
if there is no branching, then a (sub)word is stored as a sequential data structure.
WARNING! The outputs are assumed to be different from the input symbols, as they
are used as leaf nodes in the trie when constructing a transducer.
The code is separated into two parts: 1. the trie data structure,
2. transducer generation.

FLEXIBLE INPUT OUTPUT TRANSDUCER CONSTRUCTION
input words can be sequences of any type of distinct entities
similarly outputs can be of any types
internal states are nonnegtaive integers