The Support of a Recognizable Series over a Zero-sum Free, Commutative Semiring is Recognizable | Zendy

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The Support of a Recognizable Series over a Zero-sum Free, Commutative Semiring is Recognizable

Author(s) -

Daniel Kirsten

Publication year - 2011

Publication title -

acta cybernetica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.143

H-Index - 18

eISSN - 2676-993X

pISSN - 0324-721X

DOI - 10.14232/actacyb.20.2.2011.1

Subject(s) - semiring , zero (linguistics) , commutative property , series (stratigraphy) , mathematics , transformation (genetics) , automaton , discrete mathematics , pure mathematics , combinatorics , computer science , theoretical computer science , paleontology , philosophy , linguistics , biochemistry , chemistry , gene , biology

We show that the support of a recognizable series over a zero-sum free, commutative semiring is a recognizable language. We also give a sufficient and necessary condition for the existence of an effective transformation of a weighted automaton recognizing a series S over a zero-sum free, commutative semiring into an automaton recognizing the support of S.

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