Displaying similar documents to “A fully equational proof of Parikh’s theorem”

A Fully Equational Proof of Parikh's Theorem

Luca Aceto, Zoltán Ésik, Anna Ingólfsdóttir (2010)

RAIRO - Theoretical Informatics and Applications

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We show that the validity of Parikh's theorem for context-free languages depends only on a few equational properties of least pre-fixed points. Moreover, we exhibit an infinite basis of -term equations of continuous commutative idempotent semirings.

Rational semimodules over the max-plus semiring and geometric approach to discrete event systems

Stéphane Gaubert, Ricardo Katz (2004)

Kybernetika

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We introduce rational semimodules over semirings whose addition is idempotent, like the max-plus semiring, in order to extend the geometric approach of linear control to discrete event systems. We say that a subsemimodule of the free semimodule 𝒮 n over a semiring 𝒮 is rational if it has a generating family that is a rational subset of 𝒮 n , 𝒮 n being thought of as a monoid under the entrywise product. We show that for various semirings of max-plus type whose elements are integers, rational...

Finite Product of Semiring of Sets

Roland Coghetto (2015)

Formalized Mathematics

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We formalize that the image of a semiring of sets [17] by an injective function is a semiring of sets.We offer a non-trivial example of a semiring of sets in a topological space [21]. Finally, we show that the finite product of a semiring of sets is also a semiring of sets [21] and that the finite product of a classical semiring of sets [8] is a classical semiring of sets. In this case, we use here the notation from the book of Aliprantis and Border [1].

Commutative images of rational languages and the Abelian kernel of a monoid

Manuel Delgado (2010)

RAIRO - Theoretical Informatics and Applications

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Natural algorithms to compute rational expressions for recognizable languages, even those which work well in practice, may produce very long expressions. So, aiming towards the computation of the commutative image of a recognizable language, one should avoid passing through an expression produced this way. We modify here one of those algorithms in order to compute directly a semilinear expression for the commutative image of a recognizable language. We also give a second modification...