<p style='text-indent:20px;'>We construct topological invariants, called abstract weak orbit spaces, of flows and homeomorphisms on spaces. In particular, the spaces are refinements Morse graphs compact metric Reeb Hamiltonian with finitely many singular points surfaces, CW decompositions which consist unstable manifolds for closed manifolds. Though decomposition a flow is finite, interse...

Resolution is the most widely studied approach to propositional theorem proving. In developing efficient resolutionbased algorithms, dozens of variants and refinements of resolution have been studied from both the empirical and analytic sides. The most prominent of these refinements are: DP (ordered), DLL (tree), semantic, negative, linear and regular resolution. In this paper, we characterize ...

Dependently typed programming languages allow sophisticated properties of data to be expressed within the type system. Of par-ticular use in dependently typed programming are indexed types that refine data by computationally useful information. For example, the Nindexed type of vectors refines lists by their lengths. Other data types may be refined in similar ways, but programmers must produce ...