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, we establish an equivalence property of weighted Muller and weighted Büchi automata over certain semirings. DOI: 10.3103/S1066369X10010044

Dr. Matthias Dembinski is a Senior Research Fellow at the Research Institute for International Affairs (Stiftung Wissenschaft und Politik) in Ebenhausen, Germany. Prior to joining that Institute, he worked with the Nuclear Nonproliferation Project at the Peace Research Institute in Frankfurt. His most recent publications include Amerikanische Weltpolitik nach dem Ende des Ost-West-Konflikts (ed...

First, we give an alternative proof of the famous McEliece’s result about divisibility of the weights of the binary Reed-Muller codes fully relying on knowledge for Boolean functions. Second, we prove that any binary Reed-Muller code RM(r, m) contains codeword such that the highest power of 2 dividing its weight is exactly 2[(m−1)/r].