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Weighted automata are nondeterministic automata with numerical weights on transitions. They can define quantitative languages L that assign to each word w a real number L(w). In the case of infinite words, the value of a run is naturally computed as the maximum, limsup, liminf, limit average, or discounted sum of the transition weights. We study expressiveness and closure questions about these quantitative...
We present a compositional theory of system verification, where specifications assign real-numbered costs to systems. These costs can express a wide variety of quantitative system properties, such as resource consumption, price, or a measure of how well a system satisfies its specification. The theory supports the composition of systems and specifications, and the hiding of variables. Boolean refinement...
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