Solving $$\mathrm {LIA} ^\star $$ Using Approximations

Integrating Cardinality Constraints into Constraint Logic Programming with Sets

“…In a further development, Piskac and Kuncak (Piskac and Kuncak 2008) give a decision procedure for multisets with cardinality constraints by using a similar method (i.e., encoding input formulas as quantifier-free PA formulas); more recently a more efficient method based on a LIA * encoding has been proposed (Piskac 2020;Levatich et al 2020). These algorithms have been implemented in the MUNCH (Piskac and Kuncak 2010) and ssl-reachability (Piskac 2020) tools which use existing solvers to solve the various problems derived from this approach, e.g., linear integer arithmetic.…”

Verifying SQL queries using theories of tables and relations

“…The new decision procedure reduces QFB to QFPA ⋆ , which extends QFPA with formulas ū ∈ {x | ϕ}, where ϕ ∈ QFPA. Then, the QFPA ⋆ formula is translated into a QFPA formula, but with the addition of space overhead [15]. An improved decision procedure which addresses the space overhead issue by using approximations and interpolation with a set of Constrained Horn Clauses was provided in Levatich et al [15].…”

“…Then, the QFPA ⋆ formula is translated into a QFPA formula, but with the addition of space overhead [15]. An improved decision procedure which addresses the space overhead issue by using approximations and interpolation with a set of Constrained Horn Clauses was provided in Levatich et al [15]. Our work is closest to Zarba's [24], with additional support for map and filter operators.…”

“…This extension supports projection, product, and aggregate functions. SQLSolver implements algorithms similar to those in Levatich et al [15] to translate these formulas into QFPA. SQLSolver dominates other tools both in terms of performance and expressiveness of the supported SQL fragment.…”