Abstract
We consider partial Conway semirings and partial iteration semirings, both introduced by Bloom, Ésik, Kuich [2]. We develop a theory of cycle-free elements in partial iterative semirings that allows us to define cycle-free finite automata in partial iterative semirings and to prove a Kleene Theorem. We apply these results to power series over a graded monoid with discounting.
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Bloom, S.L., Ésik, Z., Kuich, W. (2009). Cycle-Free Finite Automata in Partial Iterative Semirings. In: Bozapalidis, S., Rahonis, G. (eds) Algebraic Informatics. CAI 2009. Lecture Notes in Computer Science, vol 5725. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03564-7_1
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DOI: https://doi.org/10.1007/978-3-642-03564-7_1
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