Abstract
We consider power series over a graded monoid \(M\) of finite type. We show first that, under certain conditions, the equivalence problem of power series over \(M\) with coefficients in the semiring \(\mathbb N\) of nonnegative integers can be reduced to the equivalence problem of power series over \(\{x\}^*\) with coefficients in \(\mathbb N\). This result is then applied to rational and recognizable power series over \(M\) with coefficients in \(\mathbb N\), and to rational power series over \(\Sigma ^*\) with coefficients in the semiring \(\mathbb {Q}_+\) of nonnegative rational numbers, where \(\Sigma \) is an alphabet.
Partially supported by grant no. K 108448 from the National Foundation of Hungary for Scientific Research.
Partially supported by Austrian Science Fund (FWF): grant no. I1661-N25.
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Ésik, Z., Kuich, W. (2014). On Power Series over a Graded Monoid. In: Calude, C., Freivalds, R., Kazuo, I. (eds) Computing with New Resources. Lecture Notes in Computer Science(), vol 8808. Springer, Cham. https://doi.org/10.1007/978-3-319-13350-8_4
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DOI: https://doi.org/10.1007/978-3-319-13350-8_4
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