Given a topological space ⟨X,T⟩ ∈ M, an elementary submodel of set theory, we define to be X ∩ M with topology generated by U ∩ M:U ∈ T ∩ M. We prove that if is homeomorphic to ℝ, then . The same holds for arbitrary locally compact uncountable separable metric spaces, but is independent of ZFC if “local compactness” is omitted.
Inf-Datalog extends the usual least fixpoint semantics of Datalog with greatest fixpoint semantics: we defined inf-Datalog and characterized the expressive power of various fragments of inf-Datalog in [16]. In the present paper, we study the complexity of query evaluation on finite models for (various fragments of) inf-Datalog. We deduce a unified and elementary proof that global model-checking (i.e. computing all nodes satisfying a formula in a given structure) has 1. quadratic data complexity...
Inf-Datalog extends the usual least fixpoint semantics of Datalog with greatest fixpoint semantics: we defined inf-Datalog and characterized the expressive power of various fragments of inf-Datalog in [CITE]. In the present paper, we study the complexity of query evaluation on finite models for (various fragments of) inf-Datalog. We deduce a unified and elementary proof that global model-checking (i.e. computing all nodes satisfying a formula in a given structure) has 1. quadratic data complexity...
We present an abstract equational framework for the specification of systems having both observational and computational features. Our approach is based on a clear separation between the two categories of features, and uses algebra, respectively coalgebra to formalise them. This yields a coalgebraically-defined notion of observational indistinguishability, as well as an algebraically-defined notion of reachability under computations. The relationship between the computations yielding new system...
We present an abstract equational framework for the specification of systems having both observational and computational features. Our approach is based on a clear separation between the two categories of features, and uses algebra, respectively coalgebra to formalise them. This yields a coalgebraically-defined notion of observational indistinguishability, as well as an algebraically-defined notion of reachability under computations. The relationship between the computations yielding new system states...