A translation of weighted LTL formulas to weighted Büchi automata over ω-valuation monoids
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In this paper we introduce a weighted LTL over product ω-valuation monoids that satisfy specific properties. We also introduce weighted generalized Büchi automata with ϵ-transitions, as well as weighted Büchi automata with ϵ-transitions over product ω-valuation monoids and prove that these two models are expressively equivalent and also equivalent to weighted Büchi automata already introduced in the literature. We prove that every formula of a syntactic fragment of our logic can be effectively translated to a weighted generalized Büchi automaton with ϵ-transitions. Finally, we prove that the number of states of the produced automaton is polynomial in the size of the corresponding formula.
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