2005arXiv (Cornell University)Open access

On Partially Additive Kleene Algebras

Riccardo Pucella

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Abstract

We define the notion of a partially additive Kleene algebra, which is a Kleene algebra where the + operation need only be partially defined. These structures formalize a number of examples that cannot be handled directly by Kleene algebras. We relate partially additive Kleene algebras to existing algebraic structures, by exhibiting categorical connections with Kleene algebras, partially additive categories, and closed semirings.

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We define the notion of a partially additive Kleene algebra, which is a Kleene algebra where the + operation need only be partially defined. These structures formalize a number of examples that cannot be handled directly by Kleene algebras. We relate partially additive Kleene algebras to existing algebraic structures, by exhibiting categorical connections with Kleene algebras, partially additive categories, and closed semirings.

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Available abstract

We define the notion of a partially additive Kleene algebra, which is a Kleene algebra where the + operation need only be partially defined. These structures formalize a number of examples that cannot be handled directly by Kleene algebras. We relate partially additive Kleene algebras to existing algebraic structures, by exhibiting categorical connections with Kleene algebras, partially additive categories, and closed semirings.

Key concepts: Kleene algebra, Kleene's recursion theorem, Categorical variable, Mathematics, Pure mathematics, Algebra over a field, Algebraic number, Algebraic structure

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