Geodesic
Weighted automata and weighted logic on infinite words
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2010), pp. 34-58

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We introduce weighted automata over infinite words with Muller acceptance condition and we show that their behaviors coincide with the semantics of weighted restricted MSO-sentences. Furthermore, we establish an equivalence property of weighted Muller and weighted Büchi automata over certain semirings.
Keywords: weighted logic, weighted Muller automata, infinitary formal power series, weighted Büchi automata. 
@article{IVM_2010_1_a4,
     author = {M. Droste and G. Rahonis},
     title = {Weighted automata and weighted logic on infinite words},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {34--58},
     publisher = {mathdoc},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2010_1_a4/}
}
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M. Droste; G. Rahonis. Weighted automata and weighted logic on infinite words. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2010), pp. 34-58. http://geodesic.mathdoc.fr/item/IVM_2010_1_a4/