Kleene Algebra with Hypotheses

Amina Doumane (1, 2) , Denis Kuperberg (1, 2) , Damien Pous (1, 2) , Pierre Pradic (3, 1, 2)

1 PLUME - Preuves et Langages
2 LIP - Laboratoire de l'Informatique du Parallélisme
3 MIMUW - Faculty of Mathematics, Informatics, and Mechanics [Warsaw]

We study the Horn theories of Kleene algebras and star continuous Kleene algebras, from the complexity point of view. While their equational theories coincide and are PSpace-complete, their Horn theories differ and are undecidable. We characterise the Horn theory of star continuous Kleene algebras in terms of downward closed languages and we show that when restricting the shape of allowed hypotheses, the problems lie in various levels of the arithmetical or analytical hierarchy. We also answer a question posed by Cohen about hypotheses of the form 1 = S where S is a sum of letters: we show that it is decidable.

Domaines: Logique en informatique [cs.LO]

Amina Doumane, Denis Kuperberg, Damien Pous, Pierre Pradic. Kleene Algebra with Hypotheses. 22nd International Conference on Foundations of Software Science and Computation Structures (FoSSaCS), 2019, Prague, Czech Republic. ⟨hal-02021315⟩