A Complete Classification of Tractability in RCC-5

We investigate the computational properties of the spatial algebra RCC-5 which is a restricted version of the RCC framework for spatial reasoning. The satisfiability problem for RCC-5 is known to be NP-complete but not much is known about its approximately four billion subclasses. We provide a complete classification of satisfiability for all these subclasses into polynomial and NP-complete respectively. In the process, we identify all maximal tractable subalgebras which are four in total.Comment: See http://www.jair.org/ for an online appendix and other files accompanying this articl

Reachability in Cooperating Systems with Architectural Constraints is PSPACE-Complete

The reachability problem in cooperating systems is known to be PSPACE-complete. We show here that this problem remains PSPACE-complete when we restrict the communication structure between the subsystems in various ways. For this purpose we introduce two basic and incomparable subclasses of cooperating systems that occur often in practice and provide respective reductions. The subclasses we consider consist of cooperating systems the communication structure of which forms a line respectively a star.Comment: In Proceedings GRAPHITE 2013, arXiv:1312.706

On tractability and congruence distributivity

Constraint languages that arise from finite algebras have recently been the object of study, especially in connection with the Dichotomy Conjecture of Feder and Vardi. An important class of algebras are those that generate congruence distributive varieties and included among this class are lattices, and more generally, those algebras that have near-unanimity term operations. An algebra will generate a congruence distributive variety if and only if it has a sequence of ternary term operations, called Jonsson terms, that satisfy certain equations. We prove that constraint languages consisting of relations that are invariant under a short sequence of Jonsson terms are tractable by showing that such languages have bounded relational width