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

Abstract

In this paper we introduce a weighted LTL over product $\omega$-valuation monoids that satisfy specific properties. We also introduce weighted generalized Büchi automata with $\epsilon$-transitions, as well as weighted Büchi automata with $\epsilon$-transitions over product $\omega$-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 $\epsilon$-transitions. For generalized product $\omega$-valuation monoids that satisfy specific properties we define a weighted LTL, weighted generalized Büchi automata with $\epsilon$-transitions, and weighted Büchi automata with $\epsilon$-transitions, and we prove the aforementioned results for generalized product $\omega$-valuation monoids as well. The translation of weighted LTL formulas to weighted generalized Büchi automata with $\epsilon$-transitions is now obtained for a restricted syntactical fragment of the logic.

References in corpus (1)

• Probabilistic Weighted Automata