Weight Assignment Logic

We introduce a weight assignment logic for reasoning about quantitative languages of infinite words. This logic is an extension of the classical MSO logic and permits to describe quantitative properties of systems with multiple weight parameters, e.g., the ratio between rewards and costs. We show that this logic is expressively equivalent to unambiguous weighted B\"uchi automata. We also consider an extension of weight assignment logic which is expressively equivalent to nondeterministic weighted B\"uchi automata.