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Standard automata accept or reject input words. Accordingly, an automaton induces a mapping from Σ* to the binary set {true,false}. The course will introduce multi-valued automata, which induce mappings from Σ* to richer sets of values. We will focus on lattice automata, which map input words to values from a lattice, and weighted automata, which map input words to (the set of real numbers). We describe applications of lattice automata in abstraction and model checking of multi-valued logics, and describe applications of weighted automata in the competitive analysis of online algorithms.
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