  We introduce notions of simulation between semiring-weighted automata as
models of quantitative systems. Our simulations are instances of the
categorical/coalgebraic notions previously studied by Hasuo---hence soundness
against language inclusion comes for free---but are concretely presented as
matrices that are subject to linear inequality constraints. Pervasiveness of
these formalisms allows us to exploit existing algorithms in: searching for a
simulation, and hence verifying quantitative correctness that is formulated as
language inclusion. Transformations of automata that aid search for simulations
are introduced, too. This verification workflow is implemented for the
plus-times and max-plus semirings. Furthermore, an extension to weighted tree
automata is presented and implemented.
