Streamlining Temporal Formal Verification over Columnar Databases

Recent findings demonstrate how database technology enhances the computation of formal verification tasks expressible in linear time logic for finite traces (LTLf). Human-readable declarative languages also help the common practitioner to express temporal constraints in a straightforward and accessible language. Notwithstanding the former, this technology is in its infancy, and therefore, few optimization algorithms are known for dealing with massive amounts of information audited from real systems. We, therefore, present four novel algorithms subsuming entire LTLf expressions while outperforming previous state-of-the-art implementations on top of KnoBAB, thus postulating the need for the corresponding, leading to the formulation of novel xtLTLf-derived algebraic operators

Algebraic Query Languages on Temporal Databases with Multiple Time Granularities

This paper investigates algebraic query languages on temporal databases. The data model used is a multidimensional extension of the temporal modules introduced in [WJS95]. In a multidimensional temporal module, every non-temporal fact has a timestamp that is a set ofn-ary tuples of time points. A temporal module has a set of timestamped facts and has an associated temporal granularity (or temporal type), and a temporal database is a set of multidimensional temporal modules with possibly different temporal types. Temporal algebras are proposed on this database model. Example queries and results of the paper show that the algebras are rather expressive. The operations of the algebras are organized into two groups: snapshot-wise operations and timestamp operations. Snapshot-wise operations are extensions of the traditional relational algebra operations, while timestamp operations are extensions of first-order mappings from timestamps to timestamps. Multiple temporal types are only dealt with by these timestamp operations. Hierarchies of algebras are defined in terms of the dimensions of the temporal modules in the is used to denote all the algebra queries whose input, output and intermediate modules are of dimensions at mostm,nandk, respectively. (Most temporal algebras proposed intermediate results. The symbol TALG m;n k in the literature are in TALG 1;1 1.) Equivalent hierarchies TCALCm;n k are defined in a calculus query language that is formulated by using a first-order logic with linear order. The addition of aggregation functions into the algebras is also studied