An alphabetic cone is a family of forests stable under alphabetic tree transductions, whereas we call REC-closed each family of forests closed under the operations of union, top-catenation,a-productâ€¦ (More)

We introduce a weighted logic with discounting and we establish BÃ¼chiâ€™s and Elgotâ€™s theorem for weighted automata over finite words and arbitrary commutative semirings. Then we investigate BÃ¼chi andâ€¦ (More)

We introduce weighted automata over infinite words with Muller acceptance condition and we show that their behaviors coincide with the semantics of weighted restricted MSOsentences. Furthermore, weâ€¦ (More)

We consider weighted tree automata with discounting over commutative semirings. For their behaviors we establish a Kleene theorem and an MSOlogic characterization. We introduce also weighted Mullerâ€¦ (More)

We de-ne a new type of tree transducers. The family of transformations computed by them is exactly the family of alphabetic tree relations. We call these transducers alphabetic. By takingâ€¦ (More)

We consider a first-order logic, a linear temporal logic, star-free expressions and counter-free BÃ¼chi automata, with weights, over idempotent, zerodivisor free and totally commutative completeâ€¦ (More)