Embedding Multi-Hemirings into Semirings
نویسندگان
چکیده
Weighted languages and weighted automata over multi-hemirings are capable of expressing quantitative properties of systems such as its average or discounted costs. We study the applicability of well-known semiring theory and algorithms in the field of multi-hemirings. To this end, we embed multi-hemirings into semirings and extend this embedding for weighted languages and weighted automata. We connect the rationality of a weighted multi-hemiring language with the rationality of its semiring representative, and relate the behavior of a multi-hemiring automaton and its semiring representative. From this, we derive a Kleene-Schützenberger theorem for weighted languages over multi-hemirings. Finally, we investigate the results of applying semiring algorithms to representative semiring automata.
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