Learnability and Definability in Trees and Similar Structures
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Upper bounds for a theory of queues
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
First-order and counting theories of ω-automatic structures
FOSSACS'06 Proceedings of the 9th European joint conference on Foundations of Software Science and Computation Structures
Decision procedures for queues with integer constraints
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
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Abstract: We study algebras of definable string relations-classes of regular n-ary relations that arise as the definable sets within a model whose carrier is the set of all strings. We show that the largest such algebra-the collection of regular relations-has some quite undesirable computational and model-theoretic properties. In contrast, we exhibit several definable relation algebras that have much tamer behavior: for example, they admit quantifier elimination, and have finite VC dimension. We show that the properties of a definable relation algebra are not at all determined by the one-dimensional definable sets. We give models whose definable sets are all star-free, but whose binary relations are quite complex, as well as models whose definable sets include all regular sets, but which are much more restricted and tractable than the full algebra of regular r elations.