Rational and recognisable power series
نویسنده
چکیده
2.1 Series over a graded monoid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1.1 Graded monoid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.2 Topology on K〈〈M〉〉 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Distance on K〈〈M〉〉 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Summable families . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Rational series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.1 Star of a series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Star of a proper series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Strong semirings and star of an arbitrary series . . . . . . . . . . . . . . . . . . . . . . 13 2.2.2 The family of rational series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 K-rational operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Characteristic series and unambiguous rational sets . . . . . . . . . . . . . . . . . . 16 Rational K-expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
منابع مشابه
The special subgroup of invertible non-commutative rational power series as a metric group
1: We give an easy proof of Schützenberger’s Theorem stating that non-commutative formal power series are rational if and only if they are recognisable. A byproduct of this proof is a natural metric on a subgroup of invertible rational non-commutative power series. We describe a few features of this metric group.
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