Christian Wurm | Searcharxiv

arXiv2015

Synchronous Subsequentiality and Approximations to Undecidable Problems

We introduce the class of synchronous subsequential relations, a subclass of the synchronous relations which embodies some properties of subsequential relations. If we take relations of this class as forming the possible transitions of an infinite automaton, then most decision problems (apart from membership) still remain undecidable (as they are for synchronous and subsequential rational relations), but on the positive side, they can be approximated in a meaningful way we make precise in this paper. This might make the class useful for some applications, and might serve to establish an intermediate position in the trade-off between issues of expressivity and (un)decidability.

cs.FL↗

arXiv2014

Kleene Algebras, Regular Languages and Substructural Logics

We introduce the two substructural propositional logics KL, KL+, which use disjunction, fusion and a unary, (quasi-)exponential connective. For both we prove strong completeness with respect to the interpretation in Kleene algebras and a variant thereof. We also prove strong completeness for language models, where each logic comes with a different interpretation. We show that for both logics the cut rule is admissible and both have a decidable consequence relation.

cs.LO↗