A Nivat Theorem for Weighted Alternating Automata over Commutative Semirings

In this paper, we give a Nivat-like characterization for weighted alternating automata over commutative semirings (WAFA). To purpose prove that can be characterized as the concatenation of finite tree (WFTA) and specific class homomorphism. We show series recognized by is closed under inverses homomorphisms, but not homomorphisms. logical automata, which uses MSO logic trees. Finally investigate strong connection between polynomial automata. Using corresponding result are able to ZERONESS problem with rational numbers weights decidable.