$\mathcal{T}$-semiring pairs

Continuous Semiring-Semimodule Pairs and Mixed Algebraic Systems

We associate with every commutative continuous semiring S and alphabet Σ a category whose objects are all sets and a morphism X → Y is determined by a function from X into the semiring of formal series S⟪(Y ⊎Σ) ⟫ of finite words over Y ⊎Σ, an X × Y -matrix over S⟪(Y ⊎Σ) ⟫, and a function from X into the continuous S⟪(Y ⊎Σ) ⟫-semimodule S⟪(Y ⊎Σ) ⟫ of series of ωwords over Y ⊎Σ. When S is also an...

Semiring Neighbours

In 1996 Zhou and Hansen proposed a first-order interval logic called Neighbourhood Logic (NL) for specifying liveness and fairness of computing systems and also defining notions of real analysis in terms of expanding modalities. After that, Roy and Zhou presented a sound and relatively complete Duration Calculus as an extension of NL. We present an embedding of NL into an idempotent semiring of...

Semiring Parsing

decorations of parse forests usingdynamic programming and algebraicpower series. Theoretical Computer Science.To appear.Tendeau, Frédéric. 1997b. An Earleyalgorithm for generic attribute augmentedgrammars and applications. In Proceedingsof the International Workshop on ParsingTechnologies 1997, pages 199–209.Viterbi, Andrew J. 1967. Error bounds forconvol...

Semiring of Sets

Schmets [22] has developed a measure theory from a generalized notion of a semiring of sets. Goguadze [15] has introduced another generalized notion of semiring of sets and proved that all known properties that semiring have according to the old definitions are preserved. We show that this two notions are almost equivalent. We note that Patriota [20] has defined this quasi-semiring. We propose ...

Compiling Semiring-based Constraints