Talk:Rational language

Def page pls.
I'm unable to find the def given here in any of the sources that are/were cited. Skarovitch (p.86) defines "Rational language" to be what practically everyone else calls a regular language. And the same goes for Berstel and his colleague: "The set of rational languages over A is the smallest set of subsets of A∗ containing the finite subsets and closed under union, product, and submonoid generation." JMP EAX (talk) 23:57, 17 August 2014 (UTC)

And
I'm new to this topic, but I strongly doubt the general definition attempt on this wiki page can make any sense, given the following quotes from Sakarovitch (not his long book, but his more digestible chapter in the Handbook of Weighted Automata: "Weighted automata realise power series—in contrast to ‘classical’ automata which accept languages. [...] We first characterise rational series ‘from above’ with the definition of rational operations and of closed families, and then inductively ‘from below’, with the definition of weighted rational expressions." These weighted rational expressions are not your typical formal languages because they are not [simply] over strings (unlike regular expressions). An example of weighted rational expression is $$(\frac{1}{6}a^* + \frac{1}{3}b^*)^*$$. The interpretation of this is in terms of a weighted automaton. In Sakarovitch's big book weighted rational expressions are also called "rational $$\mathbb{K}$$-expressions" (p. 399) JMP EAX (talk) 01:35, 18 August 2014 (UTC)