Incomplete MaxSAT approaches for combinatorial testing

Abstract

We present a Satisfiability (SAT)-based approach for building Mixed Covering Arrays with Constraints of minimum length, referred to as the Covering Array Number problem. This problem is central in Combinatorial Testing for the detection of system failures. In particular, we show how to apply Maximum Satisfiability (MaxSAT) technology by describing efficient encodings for different classes of complete and incomplete MaxSAT solvers to compute optimal and suboptimal solutions, respectively. Similarly, we show how to solve through MaxSAT technology a closely related problem, the Tuple Number problem, which we extend to incorporate constraints. For this problem, we additionally provide a new MaxSAT-based incomplete algorithm. The extensive experimental evaluation we carry out on the available Mixed Covering Arrays with Constraints benchmarks and the comparison with state-of-the-art tools confirm the good performance of our approaches.

Clausal Forms in MaxSAT and MinSAT

“…For a formula ϕ, let us denote by S Fm(ϕ) the set of subformulas of ϕ. Then, for each ψ ∈ S Fm(ϕ), consider a new variable y ψ , and for each formula ψ, we define the set of clauses De f (ψ) by 6 De f (x) := ∅ for x propositional variable,…”

“…MaxSAT and MinSAT have been applied in real-world domains as diverse as bioinformatics [1,2], circuit design and debugging [3], combinatorial auctions [4], combinatorial testing [5,6], community detection in complex networks [7], diagnosis [8], planning [9], scheduling [10], and team formation [11,12], among others.…”

A Complete Tableau Calculus for the Regular MaxSAT Problem

“…The development of highly competitive MaxSAT solvers (e.g. [5,14]) has allowed to apply MaxSAT to solve challenging optimization problems in various fields such as bioinformatics [22], circuit design and debugging [23], combinatorial testing [3], diagnosis [10], planning [24], scheduling [7] and team formation [21].…”

A Tableau Calculus for MaxSAT Based on Resolution

“…Although this work is mainly theoretical, it is worth mentioning that MaxSAT offers a competitive generic problem solving formalism for combinatorial optimization. For example, MaxSAT has been applied to solve optimization problems in real-world domains as diverse as combinatorial testing [1], community detection in complex networks [17],…”