  Weighted automata are non-deterministic automata where the transitions are
equipped with weights. They can model quantitative aspects of systems like
costs or energy consumption. The value of a run can be computed, for example,
as the maximum, limit average, or discounted sum of transition weights. In
multi-weighted automata, transitions carry several weights and can model, for
example, the ratio between rewards and costs, or the efficiency of use of a
primary resource under some upper bound constraint on a secondary resource.
Here, we introduce a general model for multi-weighted automata as well as a
multiweighted MSO logic. In our main results, we show that this multi-weighted
MSO logic and multi-weighted automata are expressively equivalent both for
finite and infinite words. The translation process is effective, leading to
decidability results for our multi-weighted MSO logic.
