Kleene modules and linear languages

A Kleene Theorem for Languages of Words Indexed by Linear Orderings

In a preceding paper, Bruyère and Carton introduced automata, as well as rational expressions, which allow to deal with words indexed by linear orderings. A Kleene-like theorem was proved for words indexed by countable scattered linear orderings. In this paper we extend this result to languages of words indexed by all linear orderings.

Infinitary Axiomatization of the Equational Theory of Context-Free Languages

Algebraic reasoning about programming language constructs has been a popular research topic for many years. At the propositional level, the theory of flowchart programs and linear recursion are well handled by such systems as Kleene algebra and iteration theories, systems that characterize the equational theory of the regular sets. To handle more general forms of recursion including procedures ...

An Overview of Residuated Kleene Algebras and Lattices

1. Residuated Lattices with iteration 2. Background: Semirings and Kleene algebras 3. A Gentzen system for Residuated Kleene Lattices and some reducts 4. Interpreting Kleene algebras with tests 1. Residuated Lattices with iteration This talk is mostly about Residuated Kleene Lattices, which are defined as noncommutative residuated 0,1-lattices expanded with a unary operation * that satisfies x ...

P . Bouyer and A . Petit A Kleene / Büchi − like Theorem for Clock Languages

Reasoning about Term Rewriting in Kleene Categories with Converse

This paper shows that “root-only” rewrite relations with respect to term rewriting systems can be expressed using Kleene star operations in a gs-monoidal Kleene category with converse. In our framework, we can analyze some properties of term rewriting systems by computing rewrite descendants of tree languages. As an application, we consider an infinite state model-checking problem given by a te...