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Our objective is to show a possibly interesting structure of homotopic nature appearing in persistent (co)homology. Assuming that the filtration of a simplicial set embedded in induces a multiplicative filtration on the dg algebra of simplicial cochains, w ...
Our goal is to identify families of relations that are useful for reasoning about software. We describe such families using decidable quantifier-free classes of logical constraints with a rich set of operations. A key challenge is to define such classes of ...
This article approaches the incremental view maintenance problem from an algebraic perspective. The algebraic structure of a ring of databases is constructed and extended to form a powerful aggregate query calculus. The query calculus inherits the key prop ...
We describe a decision procedure for a logic that supports 1) finite collections of elements (sets or multisets), 2) the cardinality operator, 3) a total order relation on elements, and 4) min and max operators on entire collections. Among the applications ...
We describe a family of decision procedures that extend the decision procedure for quantifier-free constraints on recursive algebraic data types (term algebras) to support recursive abstraction functions. Our abstraction functions are catamorphisms (term a ...
