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Categories of algebraic contexts equivalent to idempotent semirings and domain semirings. (English) Zbl 1364.68337

Kahl, Wolfram (ed.) et al., Relational and algebraic methods in computer science. 13th international conference, RAMiCS 2012, Cambridge, UK, September 17–20, 2012. Proceedings. Berlin: Springer (ISBN 978-3-642-33313-2/pbk). Lecture Notes in Computer Science 7560, 195-206 (2012).
Summary: A categorical equivalence between algebraic contexts with relational morphisms and join-semilattices with homomorphisms is presented and extended to idempotent semirings and domain semirings. These contexts are the Kripke structures for idempotent semirings and allow more efficient computations on finite models because they can be logarithmically smaller than the original semiring. Some examples and constructions such as matrix semirings are also considered.
For the entire collection see [Zbl 1246.68043].

MSC:

68T30 Knowledge representation
06A12 Semilattices
16Y60 Semirings
18A23 Natural morphisms, dinatural morphisms
18B99 Special categories
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References:

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