Aiming for a systematic feature extraction from time series, we introduce the iterated-sums signature over arbitrary commutative semirings. The case of tropical semiring is central, and our motivating, example. It leads to features (real-valued) series that are not easily available using existing signature-type objects. We demonstrate how extracts chronological aspects its calculation possible ...

The fundamental theorem of symmetric polynomials over rings is a classical result which states that every unital commutative ring elementary, i.e. we can express with elementary ones in unique way. does not extend directly to semirings, but do have analogous results for some special example, the tropical, extended and supertropical semirings. These all fall into larger class upper-bound In this...

Many infinite finitely generated ideal-simple commutative semirings are additively idempotent. It is not clear whether this is true in general. However, to solve the problem, one can restrict oneself only to parasemifields.

The commutative ambiguity cambG,X of a context-free grammar G with start symbol X assigns to each Parikh vector v the number of distinct leftmost derivations yielding a word with Parikh vector v. Based on the results on the generalization of Newton’s method to ω-continuous semirings [EKL07b, EKL07a, EKL10], we show how to approximate cambG,X by means of rational formal power series, and give a ...