A translation of weighted LTL formulas to weighted Büchi automata over ω-valuation monoids

英文摘要：

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 $\varepsilon$-transitions, as well as weighted Büchi automata with $\varepsilon$-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 $\varepsilon$-transitions. For generalized product $ω$-valuation monoids that satisfy specific properties we define a weighted LTL, weighted generalized Büchi automata with $\varepsilon$-transitions, and weighted Büchi automata with $\varepsilon$-transitions, and we prove the aforementioned results for generalized product $ω$-valuation monoids as well. The translation of weighted LTL formulas to weighted generalized Büchi automata with $\varepsilon$-transitions is now obtained for a restricted syntactical fragment of the logic.