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Noncommutative rational Pólya seriesBell, Jason P. ; Smertnig, DanielA (noncommutative) Pólya series over a field ▫$K$▫ is a formal power series whose nonzero coefficients are contained in a finitely generated subgroup of ▫$K^\times$▫. We show that rational Pólya ... series are unambiguous rational series, proving a 40 year old conjecture of Reutenauer. The proof combines methods from noncommutative algebra, automata theory, and number theory (specifically, unit equations). As a corollary, a rational series is a Pólya series if and only if it is Hadamard sub-invertible. Phrased differently, we show that every weighted finite automaton taking values in a finitely generated subgroup of a field (and zero) is equivalent to an unambiguous weighted finite automaton.Source: Selecta mathematica. New series. - ISSN 1022-1824 (Vol. 27, iss. 3, article no. 34, Jul. 2021, 34 str.)Type of material - article, component part ; adult, seriousPublish date - 2021Language - englishCOBISS.SI-ID - 172569603
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source: Selecta mathematica. New series. - ISSN 1022-1824 (Vol. 27, iss. 3, article no. 34, Jul. 2021, 34 str.)
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Bell, Jason P. | ![]() |
Smertnig, Daniel | 58259 |
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