Chaotic functions are often successfully embedded
into pseudorandom sequence generators.
However even if these generators 
can effectively face statistical tests
(thanks to optimized parameters), they may lose 
their chaos properties since 
they are designed using floating point numbers instead of real ones
numbers.
In a previous work, we had constructed chaos-based PRNGs
defined on  a discrete domain. In this context, proofs that are 
formally established are preserved during the execution. 
We had shown that these generators successfully pass 
the most stringent statistical tests
and we had proven that some of them are chaotic.
This work completes this task and shows that 
this whole class of PRNGS is chaotic
if and only if some given graphs of iteration are strongly connected. 
