Abstract
We introduce weighted variable automata over infinite alphabets and commutative and idempotent semirings. We prove that the class of their behaviors is closed under sum, and under scalar, Hadamard, Cauchy, and shuffle product, as well as star operation. Furthermore, we consider rational series over infinite alphabets and we state a Kleene-Schützenberger theorem.
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Pittou, M., Rahonis, G. (2014). Weighted Variable Automata over Infinite Alphabets. In: Holzer, M., Kutrib, M. (eds) Implementation and Application of Automata. CIAA 2014. Lecture Notes in Computer Science, vol 8587. Springer, Cham. https://doi.org/10.1007/978-3-319-08846-4_23
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DOI: https://doi.org/10.1007/978-3-319-08846-4_23
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