FiniteStateMachine: final_word_out: more implementations

[skropf]

See also #16191.

final_word_out is used in subsequential transducers. A transducer is said to be subsequential if it is deterministic, every state is final and it has a final output word for each final state, i.e., when reading an input and reaching some final state along some path, then the final output word of this state is appended to the output labels collected along the path.

This will facilitate various transducers, e.g., when we currently have to read a sufficiently large number of zeros in order to flush some more output.

In the following functions, final_word_out is now implemented:

• FiniteStateMachine.composition: If the output of one finite state machine is used as input of another one, then also the final output word of the first one is fed into the second one.
• FiniteStateMachine.output_projection: If the automaton which recognizes the output of a transducer is constructed, then the final output word has to be the last part of a recognized input. This is implemented by constructing a new final state and adding one transition for each final output word of the original transducer. The original final states are not final anymore.
• FiniteStateMachine.prepone_output: Here, final output words have to be considered like any other transition leaving a state.
• FiniteStateMachine.product_FiniteStateMachine: A function which handles the combination of final output words is required if there exists non-trivial final output words.
• Transducer.cartesian_product: The final output words of the new transducer consists of pairs of final output words of the original transducers.

[cheuberg]

I reviewed this earlier and added a few commits. Most of them minor, but I rewrote parts of Transducer.cartesian_product and changed the default for final_function in FiniteStateMachine.product_FiniteStateMachine.

• ​fd09b66 Minor changes in docstring
• ​3dd943d Code cleanup in prepone_output
• ​ca6ae02 FiniteStateMachine.projection: store doubly used list.
• ​a042f3a FiniteStateMachine.product_FiniteStateMachine: changed default for final_function
• ​867a804 FiniteStateMachine.product_FiniteStateMachine: minor docstring edits
• ​130bec2 FiniteStateMachine.product_FiniteStateMachine: simplify code
• ​098473d Transducer.cartesian_product: use itertools.izip_longest
• ​74e4c05 FiniteStateMachine.composition: modified docstring
• ​6e9ad7b FiniteStateMachine._composition_direct: states -> iter_states
• ​ea63af0 FiniteStateMachine._composition_direct: provide final_function

[dkrenn]

made some minor changes; please cross-review. Apart from those, this is a positive review for me, so mark it whenever you like.

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New commits:

​322991f

a couple of minor changes during review

[skropf]

All changes are fine for me. Thus, I mark it as positive_review, as suggested.