Weighted register automata and weighted logic on data words

Abstract

Data words are sequences of pairs where the first element is taken from a finite alphabet and the second element is taken from an infinite data domain. Register automata provide a widely studied model for reasoning on data words. In this paper, we investigate automata models for quantitative aspects of systems with infinite data domains, e.g., the costs of storing data on a remote server or the consumption of resources (e.g., memory, energy, time) during a data analysis. We introduce weighted register automata on data words over commutative data semirings equipped with a collection of binary data functions, and we investigate their closure properties. Unlike the other models considered in the literature, we allow data comparison by means of an arbitrary collection of binary data relations. This enables us to incorporate timed automata and weighted timed automata into our framework. In our main result, we give a logical characterization of weighted register automata by means of weighted existential monadic second-order logic; for the proof we employ a new class of determinizable visibly register automata.